Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 369: 85

Answer

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

Work Step by Step

To find the inverse of y=f(x): 1. swap x and y in the expression of the function 2. solve for y 3. replace $y $with $f^{-1}(x)$ ------------ $y=\log_{2}(x-1)$ $ x=\log_{2}(y-1)\qquad$... apply $2^{(..)}$ to both sides $ 2^{x}=y-1\qquad$... $/+1$ $y=2^{x}+1$ $f^{-1}(x)=2^{x}+1$
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