Find f(g(x)) f(x)=-4x-10 g(x)=x^2+x+9

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

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.

Apply the distributive property.

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

Multiply $- 4$ by $9$ .

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

Step 4

Subtract $10$ from $- 36$ .

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