Precalculus (6th Edition) Blitzer

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

Chapter 3 - Cumulative Review Exercises - Page 516: 13

Answer

See below:
1574216627

Work Step by Step

We have to evaluate the inverse of the function using the $f\left( x \right)=2x-4$ as follows: Take $f\left( x \right)$ $=$ $y$ , $y=2x-4$ And interchange the variables $x$ and $y$: And solve for $y$ $\begin{align} & x=2y-4 \\ & x+4=2y \\ & y=\frac{x+4}{2} \end{align}$ Replace $y$ with ${{f}^{-1}}\left( x \right)$ , ${{f}^{-1}}\left( x \right)=\frac{x+4}{2}$. Let us draw the graph as follows: Steps 1: The $x\text{-intercepts}$ and $y\text{-intercepts}$ are $\left( 4,0 \right)$ And $\left( 0,2 \right)$. And for the inverse function: The intercepts are $\left( -4,0 \right)$ and $\left( 0,2 \right)$. Step 2: Plot the intercepts and join the intercepts in the graph. The graph of the functions $f\left( x \right)=2x-4$ and ${{f}^{-1}}\left( x \right)=\frac{x+4}{2}$ in the rectangular coordinate system is: The graph of the functions $f\left( x \right)=2x-4$ and ${{f}^{-1}}\left( x \right)=\frac{x+4}{2}$ intersects the x-axis at the points $\left( 2,0 \right)$ and $\left( -4,0 \right)$, respectively.
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