Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=4-3x$
$g(x)=\dfrac{1}{3}(4-x)$
Determine $f\circ g$:
$(f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{3}(4-x)\right)=4-3\cdot \dfrac{1}{3}(4-x)=4-(4-x)=4-4+x=x$
Determine $g\circ f$:
$(g\circ f)(x)=g(f(x))=g\left(4-3x\right)=\dfrac{1}{3}(4-(4-3x))=\dfrac{1}{3}\cdot 3x=x$
We got:
$(f\circ g)(x)=(g\circ f)(x)=x$
