Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 227: 72

Answer

$a.$ and $b.$ See image below. $c.\quad f^{-1}(x)=\sqrt{16-x}$

Work Step by Step

$a. $Set up a table for several x and their function values ... for points on the graph. Joint the points. (Red graph on the image) b. Using the table in (a), plot (y,x) for each (x,y). (The points (y,x) are reflections about the line $y=x$) Joint the points. (Green graph on the image) c. $\left[\begin{array}{lll} \text{In the equation, } & & \\ \text{ replace f(x) with y} & y=16-x^{2} & x\geq 0\\ \\ \text{swap x and y} & x=16-y^{2} & \\ \\ \text{solve for y} & y^{2}=16-x & \\ & y=\sqrt{16-x} & \\ \\ \text{replace y} & & \\ \text{with }f^{-1}(x) & f^{-1}(x)=\sqrt{16-x}, & x\leq 16 \end{array}\right]$
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.