Answer
Yes.
Work Step by Step
Given $f(x)=3^{x/5}-2$ and $g(x)=5log_3(x+2)$, we have $f(g(x))=3^{(5log_3(x+2))/5}-2=x+2-2=x$ and $g(f(x))=5log_3((3^{x/5}-2)+2)=5(x/5)=x$. Thus the two functions are inverses of each other.
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions - Exercises - Page 448: 4
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter 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.
