Answer
$(g~o~f)^{-1}=\frac{1}{2}x-\frac{3}{2}$
Work Step by Step
$g~o~f=g(f(x))=g(x+4)=2(x+4)-5=2x+3~~$ (Replace $f~o~g$ by $y$)
$y=2x+3~~$ (Interchange $x$ and $y$):
$x=2y+3$
$x-3=2y$
$y=\frac{1}{2}x-\frac{3}{2}$
$(g~o~f)^{-1}=\frac{1}{2}x-\frac{3}{2}$
