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:
$(f\circ g) x =f[g(x)]=f(\dfrac{1}{4}x)=(4)(\dfrac{x}{4}) =x$
and
$(g\circ f) x = g[f(x)]=g(4x)= [\dfrac{1}{4}](4x)=x$
