Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=4x$
$g(x)=\dfrac{1}{4}x$
Determine $f\circ g$:
$(f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{4}x\right)=4\cdot\dfrac{1}{4}x=x$
Determine $g\circ f$:
$(g\circ f)(x)=g(f(x))=g\left(4x\right)=\dfrac{1}{4}\cdot 4x=x$
We got:
$(f\circ g)(x)=(g\circ f)(x)=x$
