Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises: 18

Answer

a) A horizontal line drawn across $f$ will only cross it once. $\therefore f$ is one-to-one. b) Domain: $-1\leq x\leq4$ Range: $-3\leq y\leq3$ c) $f^{-1}(2)=0$ d)$f^{-1}(0)\approx-1.7$

Work Step by Step

a) $f$ never takes the same y-value twice, so it passes the horizontal line test. b) For domain and range, refer to graph, keeping in mind that the domain and range of $f^{-1}(x)$ are those of $f(x)$ swapped. c) At $y=2, x=0\therefore f^{-1}(2)=0$ d) At $y=0, x\approx-1.7\therefore f^{-1}(0)\approx-1.7$
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