Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 10 - Cumulative Review: 40

Answer

The inverse of the given function is $\color{blue}{f^{-1}(x) = 2x-1}$.

Work Step by Step

Replace $f(x)$ with $y$ to obtain $y=\frac{x+1}{2}$. To find the inverse of this function, perform the following steps: (1) Interchange $x$ and $y$ to obtain: $x=\frac{y+1}{2}$ (2) Solve for $y$ to obtain: $x=\frac{y+1}{2} \\x(2)=y+1 \\2x=y+1 \\2x-1 =y$ (3) Replace $y$ with $f^{-1}(x)$ to obtain: $f^{-1}(x) = 2x-1$ Therefore, the inverse of the given function is $\color{blue}{f^{-1}(x) = 2x-1}$.
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