Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=2x-6$
$g(x)=\dfrac{1}{2}(x+6)$
Determine $f\circ g$:
$(f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{2}(x+6)\right)=2\cdot \dfrac{1}{2}(x+6)-6=x+6-6=x$
Determine $g\circ f$:
$(g\circ f)(x)=g(f(x))=g\left(2x-6\right)=\dfrac{1}{2}(2x-6+6)=\dfrac{1}{2}\cdot 2x=x$
We got:
$(f\circ g)(x)=(g\circ f)(x)=x$