Algebra Examples

$f (x) = x^{2} + x - 2$ $g (x) = - 4 x - 6$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- 4 x - 6)$ by substituting in the value of $g$ into $f$ .

$f (- 4 x - 6) = {(- 4 x - 6)}^{2} - 4 x - 6 - 2$

Step 3

Remove parentheses.

$f (- 4 x - 6) = {(- 4 x - 6)}^{2} - 4 x - 6 - 2$

Step 4

Simplify each term.

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Step 4.1

Rewrite ${(- 4 x - 6)}^{2}$ as $(- 4 x - 6) (- 4 x - 6)$ .

$f (- 4 x - 6) = (- 4 x - 6) (- 4 x - 6) - 4 x - 6 - 2$

Step 4.2

Expand $(- 4 x - 6) (- 4 x - 6)$ using the FOIL Method.

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Step 4.2.1

Apply the distributive property.

$f (- 4 x - 6) = - 4 x (- 4 x - 6) - 6 (- 4 x - 6) - 4 x - 6 - 2$

Step 4.2.2

Apply the distributive property.

$f (- 4 x - 6) = - 4 x (- 4 x) - 4 x \cdot - 6 - 6 (- 4 x - 6) - 4 x - 6 - 2$

Step 4.2.3

Apply the distributive property.

$f (- 4 x - 6) = - 4 x (- 4 x) - 4 x \cdot - 6 - 6 (- 4 x) - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3

Simplify and combine like terms.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Rewrite using the commutative property of multiplication.

$f (- 4 x - 6) = - 4 \cdot (- 4 x \cdot x) - 4 x \cdot - 6 - 6 (- 4 x) - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 4.3.1.2.1

Move $x$ .

$f (- 4 x - 6) = - 4 \cdot (- 4 (x \cdot x)) - 4 x \cdot - 6 - 6 (- 4 x) - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3.1.2.2

Multiply $x$ by $x$ .

$f (- 4 x - 6) = - 4 \cdot (- 4 x^{2}) - 4 x \cdot - 6 - 6 (- 4 x) - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3.1.3

Multiply $- 4$ by $- 4$ .

$f (- 4 x - 6) = 16 x^{2} - 4 x \cdot - 6 - 6 (- 4 x) - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3.1.4

Multiply $- 6$ by $- 4$ .

$f (- 4 x - 6) = 16 x^{2} + 24 x - 6 (- 4 x) - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3.1.5

Multiply $- 4$ by $- 6$ .

$f (- 4 x - 6) = 16 x^{2} + 24 x + 24 x - 6 \cdot - 6 - 4 x - 6 - 2$

Step 4.3.1.6

Multiply $- 6$ by $- 6$ .

$f (- 4 x - 6) = 16 x^{2} + 24 x + 24 x + 36 - 4 x - 6 - 2$

Step 4.3.2

Add $24 x$ and $24 x$ .

$f (- 4 x - 6) = 16 x^{2} + 48 x + 36 - 4 x - 6 - 2$

Step 5

Simplify by adding terms.

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Step 5.1

Subtract $4 x$ from $48 x$ .

$f (- 4 x - 6) = 16 x^{2} + 44 x + 36 - 6 - 2$

Step 5.2

Simplify by subtracting numbers.

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Step 5.2.1

Subtract $6$ from $36$ .

$f (- 4 x - 6) = 16 x^{2} + 44 x + 30 - 2$

Step 5.2.2

Subtract $2$ from $30$ .

$f (- 4 x - 6) = 16 x^{2} + 44 x + 28$