Answer
$(g^{-1})'(8)=\frac{1}{5}$
Work Step by Step
Since $f(2)=8$, this implies $g^{-1}(8)=2$ and so, by theorem 7, $(g^{-1})'(8)=\frac{1}{g'(g^{-1}(8))}=\frac{1}{g'(2)}=\frac{1}{5}.$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 6 - Inverse Functions - 6.1 Inverse Functions - 6.1 Exercises - Page 407: 44
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