Answer
$(g^{-1} o f^{-1})(x) = \frac{x+1}{2}$
Work Step by Step
To find the inverses, replace $f(x)$ by $x$ and $ x$ by $ f^{-1}(x)$ and solve for $ f^{-1}(x)$.
Thus $ x = f^{-1}(x)+4 ⇒ f^{-1}(x) = x-4$
And $x= 2g^{-1}(x)-5⇒ g^{-1}(x) = \frac{x+5}{2} $
So, $(g^{-1} o f^{-1})(x) = g^{-1}(f^{-1}(x)) = g^{-1}(x-4) = \frac{(x-4)+5}{2} = \frac{x+1}{2} $
