Answer
True
Work Step by Step
$$f(x)=g(x)\times e^x$$
As we know that a product of two functions can be zero if and only if either of those is equal to zero and that $e^x$ is zero for no real number, all the zeroes of f(x) are those of g(x).
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 365: 116
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