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