Find g(f(x)) f(x)=x^2-9x-11 g(x)=11x-4

$f (x) = x^{2} - 9 x - 11$ $g (x) = 11 x - 4$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 9 x - 11)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 9 x - 11) = 11 (x^{2} - 9 x - 11) - 4$

Step 3

Simplify each term.

Apply the distributive property.

$g (x^{2} - 9 x - 11) = 11 x^{2} + 11 (- 9 x) + 11 \cdot - 11 - 4$

Simplify.

Multiply $- 9$ by $11$ .

$g (x^{2} - 9 x - 11) = 11 x^{2} - 99 x + 11 \cdot - 11 - 4$

Multiply $11$ by $- 11$ .

$g (x^{2} - 9 x - 11) = 11 x^{2} - 99 x - 121 - 4$

Step 4

Subtract $4$ from $- 121$ .

$g (x^{2} - 9 x - 11) = 11 x^{2} - 99 x - 125$