Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 345: 78

-1.1665

To find the inverses, replace $f(x)$ by $x$ and $ x$ by $ f^{-1}(x)$ and solve for $ f^{-1}(x)$. Thus $x=(g^{-1}(x))^3 ⇒ g^{-1}(x) = \sqrt[3] x$ So, $(g^{-1} o g^{-1})(-4) = g^{-1}(g^{-1}(-4)) = g^{-1}(\sqrt[3] {-4}) = \sqrt[3] {\sqrt[3] {-4}} = -4^{1/9} = -2^{2/9} = -1.1665$