Prakalkulus Contoh

$f (x) = x^{\frac{1}{5}} + 7$ ; find $f^{- 1} (x)$

Langkah 1

Tuliskan $f (x) = x^{\frac{1}{5}} + 7$ sebagai sebuah persamaan.

$y = x^{\frac{1}{5}} + 7$

Langkah 2

Saling tukar variabel.

$x = y^{\frac{1}{5}} + 7$

Langkah 3

Selesaikan $y$ .

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Langkah 3.1

Tulis kembali persamaan tersebut sebagai $y^{\frac{1}{5}} + 7 = x$ .

$y^{\frac{1}{5}} + 7 = x$

Langkah 3.2

Pindahkan semua suku yang tidak mengandung $y$ ke sisi kanan dari persamaan.

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Langkah 3.2.1

Kurangkan $7$ dari kedua sisi persamaan tersebut.

$y^{\frac{1}{5}} - x = - 7$

Langkah 3.2.2

Tambahkan $x$ ke kedua sisi persamaan.

$y^{\frac{1}{5}} = - 7 + x$

Langkah 3.3

Pangkatkan setiap sisi persamaan dengan pangkat $5$ untuk menghilangkan eksponen pecahan di sisi kiri.

${(y^{\frac{1}{5}})}^{5} = {(- 7 + x)}^{5}$

Langkah 3.4

Sederhanakan bentuk eksponen.

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Langkah 3.4.1

Sederhanakan sisi kirinya.

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Langkah 3.4.1.1

Sederhanakan ${(y^{\frac{1}{5}})}^{5}$ .

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Langkah 3.4.1.1.1

Kalikan eksponen dalam ${(y^{\frac{1}{5}})}^{5}$ .

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Langkah 3.4.1.1.1.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$y^{\frac{1}{5} \cdot 5} = {(- 7 + x)}^{5}$

Langkah 3.4.1.1.1.2

Batalkan faktor persekutuan dari $5$ .

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Langkah 3.4.1.1.1.2.1

Batalkan faktor persekutuan.

$y^{\frac{1}{5} \cdot 5} = {(- 7 + x)}^{5}$

Langkah 3.4.1.1.1.2.2

Tulis kembali pernyataannya.

$y^{1} = {(- 7 + x)}^{5}$

Langkah 3.4.1.1.2

Sederhanakan.

$y = {(- 7 + x)}^{5}$

Langkah 3.4.2

Sederhanakan sisi kanannya.

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Langkah 3.4.2.1

Sederhanakan ${(- 7 + x)}^{5}$ .

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Langkah 3.4.2.1.1

Gunakan Teorema Binomial.

$y = {(- 7)}^{5} + 5 {(- 7)}^{4} x + 10 {(- 7)}^{3} x^{2} + 10 {(- 7)}^{2} x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2

Sederhanakan setiap suku.

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Langkah 3.4.2.1.2.1

Naikkan $- 7$ menjadi pangkat $5$ .

$y = - 16807 + 5 {(- 7)}^{4} x + 10 {(- 7)}^{3} x^{2} + 10 {(- 7)}^{2} x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.2

Naikkan $- 7$ menjadi pangkat $4$ .

$y = - 16807 + 5 \cdot 2401 x + 10 {(- 7)}^{3} x^{2} + 10 {(- 7)}^{2} x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.3

Kalikan $5$ dengan $2401$ .

$y = - 16807 + 12005 x + 10 {(- 7)}^{3} x^{2} + 10 {(- 7)}^{2} x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.4

Naikkan $- 7$ menjadi pangkat $3$ .

$y = - 16807 + 12005 x + 10 \cdot - 343 x^{2} + 10 {(- 7)}^{2} x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.5

Kalikan $10$ dengan $- 343$ .

$y = - 16807 + 12005 x - 3430 x^{2} + 10 {(- 7)}^{2} x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.6

Naikkan $- 7$ menjadi pangkat $2$ .

$y = - 16807 + 12005 x - 3430 x^{2} + 10 \cdot 49 x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.7

Kalikan $10$ dengan $49$ .

$y = - 16807 + 12005 x - 3430 x^{2} + 490 x^{3} + 5 \cdot - 7 x^{4} + x^{5}$

Langkah 3.4.2.1.2.8

Kalikan $5$ dengan $- 7$ .

$y = - 16807 + 12005 x - 3430 x^{2} + 490 x^{3} - 35 x^{4} + x^{5}$

Langkah 3.5

Sederhanakan $- 16807 + 12005 x - 3430 x^{2} + 490 x^{3} - 35 x^{4} + x^{5}$ .

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Langkah 3.5.1

Pindahkan $- 16807$ .

$y = 12005 x - 3430 x^{2} + 490 x^{3} - 35 x^{4} + x^{5} - 16807$

Langkah 3.5.2

Pindahkan $12005 x$ .

$y = - 3430 x^{2} + 490 x^{3} - 35 x^{4} + x^{5} + 12005 x - 16807$

Langkah 3.5.3

Pindahkan $- 3430 x^{2}$ .

$y = 490 x^{3} - 35 x^{4} + x^{5} - 3430 x^{2} + 12005 x - 16807$

Langkah 3.5.4

Pindahkan $490 x^{3}$ .

$y = - 35 x^{4} + x^{5} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807$

Langkah 3.5.5

Susun kembali $- 35 x^{4}$ dan $x^{5}$ .

$y = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807$

Langkah 4

Ganti $y$ dengan $f^{- 1} (x)$ untuk memunculkan jawaban akhir.

$f^{- 1} (x) = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807$

Langkah 5

Periksa apakah $f^{- 1} (x) = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807$ merupakan balikan dari $f (x) = x^{\frac{1}{5}} + 7$ .

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Langkah 5.1

Untuk memverifikasi balikannya, periksa apakah $f^{- 1} (f (x)) = x$ dan $f (f^{- 1} (x)) = x$ .

Langkah 5.2

Evaluasi $f^{- 1} (f (x))$ .

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Langkah 5.2.1

Tulis fungsi hasil komposit.

$f^{- 1} (f (x))$

Langkah 5.2.2

Evaluasi $f^{- 1} (x^{\frac{1}{5}} + 7)$ dengan mensubstitusikan nilai (Variabel1) ke dalam (Variabel2).

$f^{- 1} (x^{\frac{1}{5}} + 7) = {(x^{\frac{1}{5}} + 7)}^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3

Sederhanakan setiap suku.

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Langkah 5.2.3.1

Gunakan Teorema Binomial.

$f^{- 1} (x^{\frac{1}{5}} + 7) = {(x^{\frac{1}{5}})}^{5} + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2

Sederhanakan setiap suku.

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Langkah 5.2.3.2.1

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{5}$ .

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Langkah 5.2.3.2.1.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x^{\frac{1}{5} \cdot 5} + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.1.2

Batalkan faktor persekutuan dari $5$ .

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Langkah 5.2.3.2.1.2.1

Batalkan faktor persekutuan.

Langkah 5.2.3.2.1.2.2

Tulis kembali pernyataannya.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.2

Sederhanakan.

Langkah 5.2.3.2.3

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{4}$ .

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Langkah 5.2.3.2.3.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 5 x^{\frac{1}{5} \cdot 4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.3.2

Gabungkan $\frac{1}{5}$ dan $4$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 5 x^{\frac{4}{5}} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.4

Kalikan $7$ dengan $5$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.5

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{3}$ .

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Langkah 5.2.3.2.5.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{1}{5} \cdot 3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.5.2

Gabungkan $\frac{1}{5}$ dan $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{3}{5}} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.6

Naikkan $7$ menjadi pangkat $2$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{3}{5}} \cdot 49 + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.7

Kalikan $49$ dengan $10$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.8

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{2}$ .

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Langkah 5.2.3.2.8.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{1}{5} \cdot 2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.8.2

Gabungkan $\frac{1}{5}$ dan $2$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{2}{5}} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.9

Naikkan $7$ menjadi pangkat $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{2}{5}} \cdot 343 + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.10

Kalikan $343$ dengan $10$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.11

Naikkan $7$ menjadi pangkat $4$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 2401 + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.12

Kalikan $2401$ dengan $5$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 7^{5} - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.2.13

Naikkan $7$ menjadi pangkat $5$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 {(x^{\frac{1}{5}} + 7)}^{4} + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.3

Gunakan Teorema Binomial.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 ({(x^{\frac{1}{5}})}^{4} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4

Sederhanakan setiap suku.

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Langkah 5.2.3.4.1

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{4}$ .

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Langkah 5.2.3.4.1.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{1}{5} \cdot 4} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.1.2

Gabungkan $\frac{1}{5}$ dan $4$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.2

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{3}$ .

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Langkah 5.2.3.4.2.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 4 x^{\frac{1}{5} \cdot 3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.2.2

Gabungkan $\frac{1}{5}$ dan $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 4 x^{\frac{3}{5}} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.3

Kalikan $7$ dengan $4$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.4

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{2}$ .

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Langkah 5.2.3.4.4.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{1}{5} \cdot 2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.4.2

Gabungkan $\frac{1}{5}$ dan $2$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.5

Naikkan $7$ menjadi pangkat $2$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} \cdot 49 + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.6

Kalikan $49$ dengan $6$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.7

Naikkan $7$ menjadi pangkat $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 4 x^{\frac{1}{5}} \cdot 343 + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.8

Kalikan $343$ dengan $4$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 1372 x^{\frac{1}{5}} + 7^{4}) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.4.9

Naikkan $7$ menjadi pangkat $4$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 1372 x^{\frac{1}{5}} + 2401) + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.5

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 35 (28 x^{\frac{3}{5}}) - 35 (294 x^{\frac{2}{5}}) - 35 (1372 x^{\frac{1}{5}}) - 35 \cdot 2401 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.6

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.3.6.1

Kalikan $28$ dengan $- 35$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 35 (294 x^{\frac{2}{5}}) - 35 (1372 x^{\frac{1}{5}}) - 35 \cdot 2401 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.6.2

Kalikan $294$ dengan $- 35$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 35 (1372 x^{\frac{1}{5}}) - 35 \cdot 2401 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.6.3

Kalikan $1372$ dengan $- 35$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 35 \cdot 2401 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.6.4

Kalikan $- 35$ dengan $2401$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.7

Gunakan Teorema Binomial.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 ({(x^{\frac{1}{5}})}^{3} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8

Sederhanakan setiap suku.

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Langkah 5.2.3.8.1

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{3}$ .

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Langkah 5.2.3.8.1.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{1}{5} \cdot 3} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.1.2

Gabungkan $\frac{1}{5}$ dan $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.2

Kalikan eksponen dalam ${(x^{\frac{1}{5}})}^{2}$ .

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Langkah 5.2.3.8.2.1

Terapkan kaidah pangkat dan perkalian eksponen, ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 x^{\frac{1}{5} \cdot 2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.2.2

Gabungkan $\frac{1}{5}$ dan $2$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 x^{\frac{2}{5}} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.3

Kalikan $7$ dengan $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.4

Naikkan $7$ menjadi pangkat $2$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} \cdot 49 + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.5

Kalikan $49$ dengan $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 147 x^{\frac{1}{5}} + 7^{3}) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.8.6

Naikkan $7$ menjadi pangkat $3$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 147 x^{\frac{1}{5}} + 343) - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.9

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 490 (21 x^{\frac{2}{5}}) + 490 (147 x^{\frac{1}{5}}) + 490 \cdot 343 - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.10

Sederhanakan.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.3.10.1

Kalikan $21$ dengan $490$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 490 (147 x^{\frac{1}{5}}) + 490 \cdot 343 - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.10.2

Kalikan $147$ dengan $490$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 490 \cdot 343 - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.10.3

Kalikan $490$ dengan $343$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 {(x^{\frac{1}{5}} + 7)}^{2} + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.11

Tulis kembali ${(x^{\frac{1}{5}} + 7)}^{2}$ sebagai $(x^{\frac{1}{5}} + 7) (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 ((x^{\frac{1}{5}} + 7) (x^{\frac{1}{5}} + 7)) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.12

Perluas $(x^{\frac{1}{5}} + 7) (x^{\frac{1}{5}} + 7)$ menggunakan Metode FOIL.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.3.12.1

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{1}{5}} (x^{\frac{1}{5}} + 7) + 7 (x^{\frac{1}{5}} + 7)) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.12.2

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{1}{5}} x^{\frac{1}{5}} + x^{\frac{1}{5}} \cdot 7 + 7 (x^{\frac{1}{5}} + 7)) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.12.3

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{1}{5}} x^{\frac{1}{5}} + x^{\frac{1}{5}} \cdot 7 + 7 x^{\frac{1}{5}} + 7 \cdot 7) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.13

Sederhanakan dan gabungkan suku-suku sejenis.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.3.13.1

Sederhanakan setiap suku.

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Langkah 5.2.3.13.1.1

Kalikan $x^{\frac{1}{5}}$ dengan $x^{\frac{1}{5}}$ dengan menambahkan eksponennya.

Ketuk untuk lebih banyak langkah...

Langkah 5.2.3.13.1.1.1

Gunakan kaidah pangkat $a^{m} a^{n} = a^{m + n}$ untuk menggabungkan pangkat.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{1}{5} + \frac{1}{5}} + x^{\frac{1}{5}} \cdot 7 + 7 x^{\frac{1}{5}} + 7 \cdot 7) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.13.1.1.2

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{1 + 1}{5}} + x^{\frac{1}{5}} \cdot 7 + 7 x^{\frac{1}{5}} + 7 \cdot 7) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.13.1.1.3

Tambahkan $1$ dan $1$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{2}{5}} + x^{\frac{1}{5}} \cdot 7 + 7 x^{\frac{1}{5}} + 7 \cdot 7) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.13.1.2

Pindahkan $7$ ke sebelah kiri $x^{\frac{1}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{2}{5}} + 7 \cdot x^{\frac{1}{5}} + 7 x^{\frac{1}{5}} + 7 \cdot 7) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.13.1.3

Kalikan $7$ dengan $7$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{2}{5}} + 7 x^{\frac{1}{5}} + 7 x^{\frac{1}{5}} + 49) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.13.2

Tambahkan $7 x^{\frac{1}{5}}$ dan $7 x^{\frac{1}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 (x^{\frac{2}{5}} + 14 x^{\frac{1}{5}} + 49) + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.14

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 3430 (14 x^{\frac{1}{5}}) - 3430 \cdot 49 + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.15

Sederhanakan.

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Langkah 5.2.3.15.1

Kalikan $14$ dengan $- 3430$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 3430 \cdot 49 + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.15.2

Kalikan $- 3430$ dengan $49$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 (x^{\frac{1}{5}} + 7) - 16807$

Langkah 5.2.3.16

Terapkan sifat distributif.

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 12005 \cdot 7 - 16807$

Langkah 5.2.3.17

Kalikan $12005$ dengan $7$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4

Sederhanakan dengan menambahkan suku-suku.

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Langkah 5.2.4.1

Gabungkan suku balikan dalam $x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$ .

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Langkah 5.2.4.1.1

Kurangi $35 x^{\frac{4}{5}}$ dengan $35 x^{\frac{4}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 + 0 - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.2

Tambahkan $x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807$ dan $0$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.3

Tambahkan $- 10290 x^{\frac{2}{5}}$ dan $10290 x^{\frac{2}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 0 + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.4

Tambahkan $x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}}$ dan $0$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.5

Kurangi $3430 x^{\frac{2}{5}}$ dengan $3430 x^{\frac{2}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 + 0 - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.6

Tambahkan $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070$ dan $0$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.7

Kurangi $168070$ dengan $168070$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 0 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.8

Tambahkan $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}}$ dan $0$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 84035 - 16807$

Langkah 5.2.4.1.9

Tambahkan $- 84035$ dan $84035$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 0 - 16807$

Langkah 5.2.4.1.10

Tambahkan $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ dan $0$ .

Langkah 5.2.4.1.11

Kurangi $16807$ dengan $16807$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 0$

Langkah 5.2.4.1.12

Tambahkan $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ dan $0$ .

Langkah 5.2.4.2

Kurangi $980 x^{\frac{3}{5}}$ dengan $490 x^{\frac{3}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 12005 x^{\frac{1}{5}} - 490 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Langkah 5.2.4.3

Gabungkan suku balikan dalam $x + 12005 x^{\frac{1}{5}} - 490 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ .

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Langkah 5.2.4.3.1

Tambahkan $- 490 x^{\frac{3}{5}}$ dan $490 x^{\frac{3}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 0 + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Langkah 5.2.4.3.2

Tambahkan $x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}}$ dan $0$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Langkah 5.2.4.4

Kurangi $48020 x^{\frac{1}{5}}$ dengan $12005 x^{\frac{1}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x - 36015 x^{\frac{1}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Langkah 5.2.4.5

Tambahkan $- 36015 x^{\frac{1}{5}}$ dan $72030 x^{\frac{1}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 36015 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Langkah 5.2.4.6

Kurangi $48020 x^{\frac{1}{5}}$ dengan $36015 x^{\frac{1}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x - 12005 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

Langkah 5.2.4.7

Gabungkan suku balikan dalam $x - 12005 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ .

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Langkah 5.2.4.7.1

Tambahkan $- 12005 x^{\frac{1}{5}}$ dan $12005 x^{\frac{1}{5}}$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x + 0$

Langkah 5.2.4.7.2

Tambahkan $x$ dan $0$ .

$f^{- 1} (x^{\frac{1}{5}} + 7) = x$

Langkah 5.3

Evaluasi $f (f^{- 1} (x))$ .

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Langkah 5.3.1

Tulis fungsi hasil komposit.

$f (f^{- 1} (x))$

Langkah 5.3.2

Evaluasi $f (x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807)$ dengan mensubstitusikan nilai (Variabel1) ke dalam (Variabel2).

$f (x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807) = {(x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807)}^{\frac{1}{5}} + 7$

Langkah 5.4

Karena $f^{- 1} (f (x)) = x$ dan $f (f^{- 1} (x)) = x$ , maka $f^{- 1} (x) = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807$ merupakan balikan dari $f (x) = x^{\frac{1}{5}} + 7$ .

$f^{- 1} (x) = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807$