Find g(f(x)) f(x)=x+2 and g(x)=x-2

$f (x) = x + 2$ and $g (x) = x - 2$

Set up the composite result function.

$g (f (x))$

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

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

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

Subtract $2$ from $2$ .

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

Add $x$ and $0$ .

$g (x + 2) = x$