Find g(f(x)) f(x)=(x-7)/2 g(x)=2x+7

$f (x) = \frac{x - 7}{2}$ $g (x) = 2 x + 7$

Set up the composite result function.

$g (f (x))$

Evaluate $g (\frac{x - 7}{2})$ by substituting in the value of $f$ into $g$ .

$g (\frac{x - 7}{2}) = 2 (\frac{x - 7}{2}) + 7$

Cancel the common factor of $2$ .

Cancel the common factor.

$g (\frac{x - 7}{2}) = 2 (\frac{x - 7}{2}) + 7$

Rewrite the expression.

$g (\frac{x - 7}{2}) = x - 7 + 7$

Combine the opposite terms in $x - 7 + 7$ .

Add $- 7$ and $7$ .

$g (\frac{x - 7}{2}) = x + 0$

Add $x$ and $0$ .

$g (\frac{x - 7}{2}) = x$