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: 85

Answer

$f^{-1}(x)=2^{x}+1$

Work Step by Step

We are given: $f(x)=\log_{2}(x-1)$ To find the inverse, we switch $x$ and $y$ and solve for $y=\log_{2}(x-1)$ $x=\log_{2}(y-1)$ $2^{x}=2^{\log_{2}(y-1)}=y-1 $ $y=2^{x}+1$ Therefore: $f^{-1}(x)=2^{x}+1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.