## Algebra and Trigonometry 10th Edition

a) $f^{-1}(x)=\sqrt[3]{x-8}$ b) See graph c) The graph of $f^{-1}$ is the reflection of the graph of $f$ across the line $y=x$ d) $D_f=(-\infty,\infty),R_f=(-\infty,\infty)$ $D_{f^{-1}}=(-\infty,\infty),R_{f^{-1}}=(-\infty,\infty)$
We are given the function: $f(x)=x^3+8$ $y=x^3+8$ a) Determine the inverse $f^{-1}$. Interchange $x$ and $y$: $x=y^3+8$ $y^3=x-8$ $y=\sqrt[3]{x-8}$ $f^{-1}(x)=\sqrt[3]{x-8}$ b) Graph both functions. c) The graph of the function $f^{-1}$ is the reflection of the graph of $f$ across the line $y=x$. d) Determine the domain and range of $f$: $D_f=(-\infty,\infty)$ $R_f=(-\infty,\infty)$ Determine the domain and range of $f^{-1}$: $D_{f^{-1}}=(-\infty,\infty)$ $R_{f^{-1}}=(-\infty,\infty)$