Trigonometry Examples

$s (x) = x - 7$ , $t (x) = 4 x^{2} - x + 3$

Step 1

Set up the composite result function.

$t (s (x))$

Step 2

Evaluate $t (x - 7)$ by substituting in the value of $s$ into $t$ .

$t (x - 7) = 4 {(x - 7)}^{2} - (x - 7) + 3$

Step 3

Simplify each term.

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Step 3.1

Rewrite ${(x - 7)}^{2}$ as $(x - 7) (x - 7)$ .

$t (x - 7) = 4 ((x - 7) (x - 7)) - (x - 7) + 3$

Step 3.2

Expand $(x - 7) (x - 7)$ using the FOIL Method.

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Step 3.2.1

Apply the distributive property.

$t (x - 7) = 4 (x (x - 7) - 7 (x - 7)) - (x - 7) + 3$

Step 3.2.2

Apply the distributive property.

$t (x - 7) = 4 (x \cdot x + x \cdot - 7 - 7 (x - 7)) - (x - 7) + 3$

Step 3.2.3

Apply the distributive property.

$t (x - 7) = 4 (x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7) - (x - 7) + 3$

Step 3.3

Simplify and combine like terms.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply $x$ by $x$ .

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

Step 3.3.1.2

Move $- 7$ to the left of $x$ .

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

Step 3.3.1.3

Multiply $- 7$ by $- 7$ .

$t (x - 7) = 4 (x^{2} - 7 x - 7 x + 49) - (x - 7) + 3$

Step 3.3.2

Subtract $7 x$ from $- 7 x$ .

$t (x - 7) = 4 (x^{2} - 14 x + 49) - (x - 7) + 3$

Step 3.4

Apply the distributive property.

$t (x - 7) = 4 x^{2} + 4 (- 14 x) + 4 \cdot 49 - (x - 7) + 3$

Step 3.5

Simplify.

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Step 3.5.1

Multiply $- 14$ by $4$ .

$t (x - 7) = 4 x^{2} - 56 x + 4 \cdot 49 - (x - 7) + 3$

Step 3.5.2

Multiply $4$ by $49$ .

$t (x - 7) = 4 x^{2} - 56 x + 196 - (x - 7) + 3$

Step 3.6

Apply the distributive property.

$t (x - 7) = 4 x^{2} - 56 x + 196 - x + 7 + 3$

Step 3.7

Multiply $- 1$ by $- 7$ .

$t (x - 7) = 4 x^{2} - 56 x + 196 - x + 7 + 3$

Step 4

Simplify by adding terms.

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Step 4.1

Subtract $x$ from $- 56 x$ .

$t (x - 7) = 4 x^{2} - 57 x + 196 + 7 + 3$

Step 4.2

Simplify by adding numbers.

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Step 4.2.1

Add $196$ and $7$ .

$t (x - 7) = 4 x^{2} - 57 x + 203 + 3$

Step 4.2.2

Add $203$ and $3$ .

$t (x - 7) = 4 x^{2} - 57 x + 206$