College Algebra 7th Edition

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

Chapter 2, Functions - Chapter 2 Review - Exercises: 96

Answer

$f^{-1}(x)= \frac{1}{2}(3x-1)$

Work Step by Step

We are given: $f(x)=\frac{2x+1}{3}$ To find the inverse function, we switch $x$ and $y$ and solve for $y$: $y=\frac{2x+1}{3}$ $x=\frac{2y+1}{3}$ $3x=2y+1$ $3x-1=2y$ $y=\frac{1}{2}(3x-1)$ Thus the inverse is: $f^{-1}(x)= \frac{1}{2}(3x-1)$
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