Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 293: 78

Answer

The domain of the inverse function $f^{-1}(x)$ is: $[5,\infty)$ The range of the inverse function $f^{-1}(x)$ is: $[0,\infty)$.

Work Step by Step

If a function $f(x)$ is one-to-one, then for all $y=f(x)$ there is only one $x$. When finding the inverse of the function, the $x$ and $y$ values get switched. The domain of the function $f(x)$ becomes the range of the inverse function and the range of the inverse function $f^{-1}(x)$ becomes the domain of the function $f(x)$. Thus, the domain of the inverse function $f^{-1}(x)$ is: $[5,\infty)$ The range of the inverse function $f^{-1}(x)$ is: $[0,\infty)$.
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