Answer
32
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, $(f^{-1} \circ g^{-1})(1) = f^{-1}(g^{-1}(1)) = f^{-1}(\sqrt[3] 1) = f^{-1}(1) =8(1+3) = 32 $
