Find g(f(x)) f(x)=2x+4 , g(x)=4-x

$f (x) = 2 x + 4$ , $g (x) = 4 - x$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x + 4)$ by substituting in the value of $f$ into $g$ .

$g (2 x + 4) = 4 - (2 x + 4)$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x + 4) = 4 - (2 x) - 1 \cdot 4$

Multiply $2$ by $- 1$ .

$g (2 x + 4) = 4 - 2 x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$g (2 x + 4) = 4 - 2 x - 4$

Step 4

Combine the opposite terms in $4 - 2 x - 4$ .

Subtract $4$ from $4$ .

$g (2 x + 4) = - 2 x + 0$

Add $- 2 x$ and $0$ .

$g (2 x + 4) = - 2 x$