Answer
$$(f\circ g)(x)=12x-13,$$
$$(g\circ f)(x)=12x+3.$$
$f$ and $g$ are not inverses of each other.
Work Step by Step
Since $f(x)=3 x+2, g(x)=4 x-5$, we have
$$(f\circ g)(x)=f(g(x))=f(4x-5)=3(4x-5)+2=12x-13,$$
and
$$(g\circ f)(x)=g(f(x))=g(3x+2)=4(3x+2)-5=12x+3.$$
Since $(f\circ g)(x)\neq x$ and $(g\circ g
f)(x)\neq x$, then $f$ and $g$ are not inverses of each other.