Answer
$(-4,4)$.
Work Step by Step
The domain requirement for $f(x)=log_5(16-x^2)$ is $16-x^2\gt0$ which gives $-4\lt x\lt4$ or $(-4,4)$.
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 Functions: Domains and Defining Equations - Exercises - Page 486: 9
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