Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises - Page 37: 75

$f^{-1}(x)=\sqrt[3] x-1$ $D_{f^{-1}}=(-\infty,\infty)$ $R_{f^{-1}}=(-\infty,\infty)$

We are given the function: $f(x)=(x+1)^3$ The domain of and range of $f$ are: $D_f=(-\infty,\infty)$ $R_f=(-\infty,\infty)$ Determine the inverse $f^{-1}$: $y=(x+1)^3$ $x=(y+1)^3$ (we switched $x$ and $y$) $\sqrt[3] x=y+1$ $y=\sqrt[3] x-1$ $f^{-1}(x)=\sqrt[3] x-1$ The domain of and range of $f^{-1}$ are: $D_{f^{-1}}=(-\infty,\infty)$ $R_{f^{-1}}=(-\infty,\infty)$