## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 8 - Cumulative Review Exercises - Page 952: 9

#### Answer

The inverse function is, ${{f}^{-1}}\left( x \right)=\frac{1}{4}\left( {{x}^{2}}+7 \right)$

#### Work Step by Step

Consider the given function, $y=\sqrt{4x-7}$ Square both sides to get, \begin{align} & {{y}^{2}}=4x-7 \\ & x=\frac{1}{4}\left( {{y}^{2}}+7 \right) \end{align} Therefore, ${{f}^{-1}}\left( x \right)=\frac{1}{4}\left( {{x}^{2}}+7 \right)$

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