Precalculus Examples

$f (x) = x^{2} - 5 x + 2$ $g (x) = - 4 x - 7$ Find: $g (f (x))$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 5 x + 2)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 5 x + 2) = - 4 (x^{2} - 5 x + 2) - 7$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (x^{2} - 5 x + 2) = - 4 x^{2} - 4 (- 5 x) - 4 \cdot 2 - 7$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 5$ by $- 4$ .

$g (x^{2} - 5 x + 2) = - 4 x^{2} + 20 x - 4 \cdot 2 - 7$

Step 3.2.2

Multiply $- 4$ by $2$ .

$g (x^{2} - 5 x + 2) = - 4 x^{2} + 20 x - 8 - 7$

Step 4

Subtract $7$ from $- 8$ .

$g (x^{2} - 5 x + 2) = - 4 x^{2} + 20 x - 15$