College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises: 84

Answer

$f^{-1}(x)= \frac{\ln x}{\ln 3}-1$

Work Step by Step

We are given: $f(x)=3^{x+1}$ To find the inverse, we switch $x$ and $y$ and solve for $y=3^{x+1}$ $x=3^{y+1}$ $\ln x=\ln(3^{y+1})$ $\ln x=(y+1)\ln 3$ $y+1= \frac{\ln x}{\ln 3}$ $y=\frac{\ln x}{\ln 3}-1$ Therefore: $f^{-1}(x)= \frac{\ln x}{\ln 3}-1$
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