Precalculus Examples

$f (x) = x^{2} - x + 11$ $g (x) = - x - 4$ Find: $((g \circ f)) (x)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - x + 11)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - x + 11) = - (x^{2} - x + 11) - 4$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (x^{2} - x + 11) = - x^{2} + x - 1 \cdot 11 - 4$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- - x$ .

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Step 3.2.1.1

Multiply $- 1$ by $- 1$ .

$g (x^{2} - x + 11) = - x^{2} + 1 x - 1 \cdot 11 - 4$

Step 3.2.1.2

Multiply $x$ by $1$ .

$g (x^{2} - x + 11) = - x^{2} + x - 1 \cdot 11 - 4$

Step 3.2.2

Multiply $- 1$ by $11$ .

$g (x^{2} - x + 11) = - x^{2} + x - 11 - 4$

Step 4

Subtract $4$ from $- 11$ .

$g (x^{2} - x + 11) = - x^{2} + x - 15$