Precalculus (6th Edition) Blitzer

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

Chapter 7 - Cumulative Review Exercises - Page 880: 26

Answer

The graph is shown below:
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Work Step by Step

We have to plot the graph of $ f\left( x \right)=2x-4$; replace $ f\left( x \right)$ and substitute y in place of $ f\left( x \right)$; then evaluate the value of the y variable for each value of the x variable or the value of the x variable for each value of the y variable. To find the value of the y-intercept, substitute $ x=0$ as given below: $\begin{align} & y=2x-4 \\ & =2\left( 0 \right)-4 \\ & =0-4 \\ & =-4 \end{align}$ To find the value of the x-intercept, substitute $ y=0$ as given below: $\begin{align} & y=2x-4 \\ & 0=2x-4 \\ & 2x=4 \\ & x=2 \end{align}$ Therefore, plot the intercepts $\left( 0,-4 \right)\text{ and }\left( 2,0 \right)$ and draw a line passing through these points to get the graph of equation $ f\left( x \right)=2x-4$. To compute the value of ${{f}^{-1}}$, rewrite the equation $ y=2x-4$ in terms of $ x $: $\begin{align} & y=2x-4 \\ & 2x=y+4 \\ & x=\frac{y+4}{2} \end{align}$ Now, put x in place of y and ${{f}^{-1}}$ in place of x: ${{f}^{-1}}=\frac{x+4}{2}$ Also, in order to plot the graph of ${{f}^{-1}}=\frac{x+4}{2}$, put y in place of ${{f}^{-1}}$ and evaluate the value of the y variable for each value of the x variable: To find the value of the y-intercept, substitute $ x=0$ as given below: $\begin{align} & y=\frac{x+4}{2} \\ & y=\frac{0+4}{2} \\ & =\frac{4}{2} \\ & =2 \end{align}$ To find the value of the x-intercept, substitute $ y=0$ as given below: $\begin{align} & y=\frac{x+4}{2} \\ & 0=\frac{x+4}{2} \\ & x+4=0 \\ & x=-4 \end{align}$ Therefore, plot the intercepts $\left( 0,2 \right)\text{ and }\left( -4,0 \right)$ and draw a line passing through these points to get the graph of the equation ${{f}^{-1}}=\frac{x+4}{2}$.
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