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

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

Set up the composite result function.

$f (g (x))$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Subtract $7$ from $7$ .

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

Add $x$ and $0$ .

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