Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Cumulative Review Exercises - Page 1181: 17


The inverse function, ${{f}^{-1}}\left( x \right)$ for $f\left( x \right)=7x-1$ is $\frac{x}{7}+\frac{1}{7}$.

Work Step by Step

Consider the provided function, $f\left( x \right)=7x-1$ Follow the steps to find an inverse of the function to get the inverse of $f\left( x \right)=7x-1$. Step 1: Replace $f\left( x \right)$ with $y$. $y=7x-1$ Step 2: Interchange $y$ and $x$. $x=7y-1$ Step 3: Solve for $y$. $\begin{align} & x=7y-1 \\ & x+1=7y-1+1 \\ & x+1=7y \\ & \frac{x+1}{7}=y \end{align}$ Step 4: Replace $y$ with ${{f}^{-1}}\left( x \right)$. ${{f}^{-1}}\left( x \right)=\frac{x+1}{7}$ Thus, the inverse function for $f\left( x \right)=7x-1$ is ${{f}^{-1}}\left( x \right)=\frac{x}{7}+\frac{1}{7}$.
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