Answer
0
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 = \frac{1}{8}f^{-1}(x)-3 ⇒f^{-1}(x)= 8(x+3)$
And $x=(g^{-1}(x))^3 ⇒ g^{-1}(x) = \sqrt[3] x$
So, $(g^{-1} o f^{-1})(-3) = g^{-1}(f^{-1}(-3)) = g^{-1}(8(3-3)) = g^{-1}(0) =\sqrt[3] 0 =0 $
