Answer
$$\frac{1}{12}.$$
Work Step by Step
Since $g(x)$ is the inverse of $f(x)$, then $g(8)=g(f(-1))=-1$ and hence
$$g'(x)=\frac{1}{f'(g(x))}\Longrightarrow g'(8)=\frac{1}{f'(-1)}=\frac{1}{12}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 10
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