Precalculus Examples

If $h (x) = x - 7$ and $g (x) = x^{2}$ ; which expression is equivalent to $((g \circ h)) (5)$ ?

Step 1

Set up the composite result function.

$g (h (x))$

Step 2

Evaluate $g (x - 7)$ by substituting in the value of $h$ into $g$ .

$g (x - 7) = {(x - 7)}^{2}$

Step 3

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

$g (x - 7) = (x - 7) (x - 7)$

Step 4

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

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Step 4.1

Apply the distributive property.

$g (x - 7) = x (x - 7) - 7 (x - 7)$

Step 4.2

Apply the distributive property.

$g (x - 7) = x \cdot x + x \cdot - 7 - 7 (x - 7)$

Step 4.3

Apply the distributive property.

$g (x - 7) = x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $x$ by $x$ .

$g (x - 7) = x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7$

Step 5.1.2

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

$g (x - 7) = x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7$

Step 5.1.3

Multiply $- 7$ by $- 7$ .

$g (x - 7) = x^{2} - 7 x - 7 x + 49$

Step 5.2

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

$g (x - 7) = x^{2} - 14 x + 49$

Step 6

Evaluate the result function by replacing $x$ with $5$ in the function.

${(5)}^{2} - 14 \cdot 5 + 49$

Step 7

Simplify the evaluated function.

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Step 7.1

Simplify each term.

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Step 7.1.1

Raise $5$ to the power of $2$ .

$25 - 14 \cdot 5 + 49$

Step 7.1.2

Multiply $- 14$ by $5$ .

$25 - 70 + 49$

Step 7.2

Simplify by adding and subtracting.

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Step 7.2.1

Subtract $70$ from $25$ .

$- 45 + 49$

Step 7.2.2

Add $- 45$ and $49$ .

$4$