Precalculus Examples

$f (x) = x^{2} - 7 x - 9$ $g (x) = - 5 x - 11$ Find: $((g \circ f)) (x)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 7 x - 9)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 7 x - 9) = - 5 (x^{2} - 7 x - 9) - 11$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (x^{2} - 7 x - 9) = - 5 x^{2} - 5 (- 7 x) - 5 \cdot - 9 - 11$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 7$ by $- 5$ .

$g (x^{2} - 7 x - 9) = - 5 x^{2} + 35 x - 5 \cdot - 9 - 11$

Step 3.2.2

Multiply $- 5$ by $- 9$ .

$g (x^{2} - 7 x - 9) = - 5 x^{2} + 35 x + 45 - 11$

Step 4

Subtract $11$ from $45$ .

$g (x^{2} - 7 x - 9) = - 5 x^{2} + 35 x + 34$