Find g(f(x)) f(x)=2x-5 g(x)=1/2(x+5)

$f (x) = 2 x - 5$ $g (x) = \frac{1}{2} (x + 5)$

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 $g$ .

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

Step 3

Combine the opposite terms in $(2 x - 5) + 5$ .

Add $- 5$ and $5$ .

$g (2 x - 5) = \frac{1}{2} \cdot (2 x + 0)$

Add $2 x$ and $0$ .

$g (2 x - 5) = \frac{1}{2} \cdot (2 x)$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$g (2 x - 5) = \frac{1}{2} \cdot (2 (x))$

Cancel the common factor.

$g (2 x - 5) = \frac{1}{2} \cdot (2 x)$

Rewrite the expression.

$g (2 x - 5) = x$