Find g(f(x)) f(x)=x+5 , g(x)=-4x+10

$f (x) = x + 5$ , $g (x) = - 4 x + 10$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x + 5)$ by substituting in the value of $f$ into $g$ .

$g (x + 5) = - 4 (x + 5) + 10$

Step 3

Simplify each term.

Apply the distributive property.

$g (x + 5) = - 4 x - 4 \cdot 5 + 10$

Multiply $- 4$ by $5$ .

$g (x + 5) = - 4 x - 20 + 10$

Step 4

Add $- 20$ and $10$ .

$g (x + 5) = - 4 x - 10$