Precalculus (6th Edition) Blitzer

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

Chapter 8 - Section 8.2 - Inconsistent and Dependent Systems and Their Applications - Exercise Set - Page 905: 48


The inverse of the function is ${{f}^{-1}}\left( x \right)=\frac{x+4}{3}$.

Work Step by Step

Let $f\left( x \right)=y$ This implies, $y=3x-4$. Now, by interchanging x and y, we get: $x=3y-4$ Solve for y. Add 4 to both sides in the above equation: $\begin{align} & x+4=3y-4+4 \\ & x+4=3y \end{align}$ Now, divide the above equation by 3: $\frac{x+4}{3}=\frac{3y}{3}$ This gives: $y=\frac{x+4}{3}$. Replace y with ${{f}^{-1}}\left( x \right)$. Therefore, ${{f}^{-1}}\left( x \right)=\frac{x+4}{3}$ Therefore, the inverse of the function $f\left( x \right)=3x-4$ is $\frac{x+4}{3}$. .
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