Precalculus Examples

$f (x) = - 4 x - 10$ $g (x) = x^{2} + x + 9$ Find: $f (g (x))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{2} + x + 9) = - 4 (x^{2} + x + 9) - 10$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x^{2} + x + 9) = - 4 x^{2} - 4 x - 4 \cdot 9 - 10$

Step 3.2

Multiply $- 4$ by $9$ .

$f (x^{2} + x + 9) = - 4 x^{2} - 4 x - 36 - 10$

Step 4

Subtract $10$ from $- 36$ .

$f (x^{2} + x + 9) = - 4 x^{2} - 4 x - 46$