Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=-\dfrac{3}{2}x-4$
$g(x)=-\dfrac{2x+8}{3}$
Compute $f\circ g$ and $g\circ f$:
$(f\circ g)(x)=f(g(x))=f\left(-\dfrac{2x+8}{3}\right)=-\dfrac{3}{2}\left(-\dfrac{2x+8}{3}\right)-4=x+4-4=x$
$(g\circ f)(x)=f(g(x))=g\left(-\dfrac{3}{2}x-4\right)=-\dfrac{2\left(-\dfrac{3}{2}x-4\right)+8}{3}=-\dfrac{-3x-8+8}{3}=-\dfrac{-3x}{3}=x$
We get:
$(f\circ g)(x)=(g\circ f)(x)=x$,
therefore $f$ and $g$ are inverse functions.