Answer
g(7)=1
g'(7)=\frac{1}{5}
Work Step by Step
f(x)=7 ⟹ x^{3}+2x+4=7 x^{3}+2x-3=0 ⟹ x=1
As g is the inverse of f, f(1)=7 means that g(7)=1
f'(x)=3x^{2}+2
g'(7)=\frac{1}{f'(g(7))}=\frac{1}{3\times1^{2}+2}=\frac{1}{5}
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 - 7.2 Inverse Functions - Exercises - Page 335: 31
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