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 - Page 67: 57


a) $x\gt\ln3$ b)$f^{-1}(x)=\ln(e^x+3)$ Domain: all real x

Work Step by Step

a) $e^x-3\gt0$ $e^x\gt3$ $x\gt\ln3$ b) $y=f(x)=\ln(e^x-3)$ $e^x-3=e^y$ $e^x=e^y+3$ $x=\ln(e^y+3)$ $y\rightleftharpoons x$: $f^{-1}(x)=y=\ln(e^x+3)$ $\because e^x+3\gt0$ for all real x, the domain is all real x
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