Answer
True
Work Step by Step
$$g(f(x))=ln(2+e^x-2) = ln(e^x)=x$$
$$f(g(x))=2+e^{ln(x-2)}=2+(x-2) =x$$
Therefore, $$f(g(x))=g(f(x))=x$$ and hence f and g are inverses of each other
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: 113
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