Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 227: 63

$f^{-1}(x)=\sqrt[6]{x}$

$f(x)=x^{6}$ $,$ $x\ge0$ Rewrite this expression as $y=x^{6}$ and solve for $x$: $y=x^{6}$ $x^{6}=y$ Take the sixth root of both sides: $\sqrt[6]{x^{6}}=\sqrt[6]{y}$ $x=\sqrt[6]{y}$ Interchange $x$ and $y$: $y=\sqrt[6]{x}$ The inverse of the original function is $f^{-1}(x)=\sqrt[6]{x}$