Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 261: 2

a) $g(x)$ has an inverse. b) $g^{-1}(x)=\sqrt[3]{x}$

a) A function must be one-to-one to have an inverse. Out of the given function, only $g(x)=x^3$ is one-to-one, so it has an inverse. b) The inverse of the cubic function is the third root function. Thus, we can write: $g(x)=x^3$ $g^{-1}(x)=\sqrt[3]{x}$