Find g(f(x)) f(x)=2x+11 and g(x)=-3x-22

$f (x) = 2 x + 11$ and $g (x) = - 3 x - 22$

Set up the composite result function.

$g (f (x))$

Evaluate $g (2 x + 11)$ by substituting in the value of $f$ into $g$ .

$g (2 x + 11) = - 3 (2 x + 11) - 22$

Simplify each term.

Apply the distributive property.

$g (2 x + 11) = - 3 (2 x) - 3 \cdot 11 - 22$

Multiply $2$ by $- 3$ .

$g (2 x + 11) = - 6 x - 3 \cdot 11 - 22$

Multiply $- 3$ by $11$ .

$g (2 x + 11) = - 6 x - 33 - 22$

Subtract $22$ from $- 33$ .

$g (2 x + 11) = - 6 x - 55$