Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Review - Exercises - Page 234: 102

Answer

a. Yes, it is a one-to-one function b. See graph below in purple c. See graph below in blue d. $(x-1)^4 = f^{-1} (x)$

Work Step by Step

a. $f(x) = 1 + \sqrt[4] {x}$ $f(p) = 1 + \sqrt[4] {p}$ $f(q) = 1 + \sqrt[4] {q}$ $f(p) = f(q)$ $1 + \sqrt[4] {p} = 1 + \sqrt[4] {q}$ $\sqrt[4]{p} = \sqrt[4] {q}$ $p=q$ Thus, it is a one-to-one function b. See graph below. This graph will be in purple $f(x) = 1 + \sqrt[4] {x}$ c. This question asks for the graph of the inverse of f(x). See graph below. This graph will be in blue. d. To find the inverse of f(x), reflect the equation over the line y=x $x = 1 + \sqrt[4] {y}$ $x-1 = \sqrt[4]{y}$ $(x-1)^4 = f^{-1} (x)$
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.