Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 418: 75

Answer

(a) $ f^{-1}(x)=x^2-6, x\ge0$ (b) see graph (c) $f(x)$ domain $[-6,\infty)$ and range $[0,\infty)$, $f^{-1}(x)$ domain $[0,\infty)$ and range $[-6,\infty)$.

Work Step by Step

(a) This function $f(x)=\sqrt {x+6}, x\ge-6$ is one-to-one. Find the inverse as the following: $y=\sqrt {x+6}\longrightarrow x=y^2-6\longrightarrow f^{-1}(x)=x^2-6, x\ge0$ (b) see graph (c) $f(x)$ domain $[-6,\infty)$ and range $[0,\infty)$, $f^{-1}(x)$ domain $[0,\infty)$ and range $[-6,\infty)$.
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