Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.2 - Inverse Functions - Exercise Set - Page 851: 23

Answer

$f^{-1}(x)=x-4$ (the inverse is blue on the graph)

Work Step by Step

Step 1: Replace $f(x)$ with $y$. $y=x+4$ Step 2: Interchange $x$ and $y$. $x=y+4$ Step 3: Solve the equation for $y$. $ x=y+4,\qquad$ ... subtract 4, $x-4=y$ Step 4: Replace y with the notation $f^{-1}(x)$. $f^{-1}(x)=x-4$ Graphing $f(x)=x+4,$ the y-intercept is at $(0,4)$, the x-intercept is when $\left[\begin{array}{l} 0=x+4\\ x=-4 \end{array}\right]$, at the point (-4,0) Plot the two points and draw a straight line through them. Graphing $f^{-1}(x)=x-4,$ the y-intercept is at $(0,-4)$, the x-intercept is when $\left[\begin{array}{l} 0=x-4\\ x=4 \end{array}\right]$, at the point (4,0) Plot the two points and draw a straight line through them. You may want to graph the line $y=x$ with a dashed line, to show the symmetry.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.