Find g(f(x)) f(x)=2x+5 , g(x)=5-x

$f (x) = 2 x + 5$ , $g (x) = 5 - x$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x + 5)$ by substituting in the value of $f$ into $g$ .

$g (2 x + 5) = 5 - (2 x + 5)$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x + 5) = 5 - (2 x) - 1 \cdot 5$

Multiply $2$ by $- 1$ .

$g (2 x + 5) = 5 - 2 x - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$g (2 x + 5) = 5 - 2 x - 5$

Step 4

Combine the opposite terms in $5 - 2 x - 5$ .

Subtract $5$ from $5$ .

$g (2 x + 5) = - 2 x + 0$

Add $- 2 x$ and $0$ .

$g (2 x + 5) = - 2 x$