Answer
See the verification below.
Work Step by Step
The functions $f(x)$ and $g(x)$ are known as inverse functions. Thus, we simplify
$(f\circ g) (x)=(g\circ f) (x)$ or, $f[g(x)]=g[f(x)]$
as follows:
$(f\circ g) (x) =f[g(x)]=f [\dfrac{(x+6)}{2}]=(2) [\dfrac{(x+6)}{2}]-6 =x+6-6=x$
and
$(g\circ f) (x) = g[f(x)]=g(2x-6)=\dfrac{1}{2}[(2x-6)+6]=\dfrac{1}{2}(2x)=x$
Hence, verified.
