Find g(f(x)) f(x)=x^2-x+14 g(x)=-5x-8

$f (x) = x^{2} - x + 14$ $g (x) = - 5 x - 8$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - x + 14)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - x + 14) = - 5 (x^{2} - x + 14) - 8$

Step 3

Simplify each term.

Apply the distributive property.

$g (x^{2} - x + 14) = - 5 x^{2} - 5 (- x) - 5 \cdot 14 - 8$

Simplify.

Multiply $- 1$ by $- 5$ .

$g (x^{2} - x + 14) = - 5 x^{2} + 5 x - 5 \cdot 14 - 8$

Multiply $- 5$ by $14$ .

$g (x^{2} - x + 14) = - 5 x^{2} + 5 x - 70 - 8$

Step 4

Subtract $8$ from $- 70$ .

$g (x^{2} - x + 14) = - 5 x^{2} + 5 x - 78$