Algebra and Trigonometry 10th Edition

Published by Cengage Learning

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 229: 49

Answer

a) $f^{-1}(x)=\dfrac{4}{x}$ b) See graph c) The graph of $f^{-1}$ is the reflection of the graph of $f$ across the line $y=x$. d) $D_f=(-\infty,0)\cup(0,\infty),R_f=(-\infty,0)\cup(0,\infty)$ $D_{f^{-1}}=(-\infty,0)\cup(0,\infty),R_{f^{-1}}=(-\infty,0)\cup(0,\infty)$

Work Step by Step

We are given the function: $f(x)=\dfrac{4}{x}$ $y=\dfrac{4}{x}$ a) Determine the inverse $f^{-1}$. Interchange $x$ and $y$: $x=\dfrac{4}{y}$ $xy=4$ $y=\dfrac{4}{x}$ $f^{-1}(x)=\dfrac{4}{x}$ 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 $f$: $D_f=(-\infty,0)\cup(0,\infty)$ $R_f=(-\infty,0)\cup(0,\infty)$ Determine the domain and range of $f^{-1}$: $D_{f^{-1}}=(-\infty,0)\cup(0,\infty)$ $R_{f^{-1}}=(-\infty,0)\cup(0,\infty)$

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