Differentiation Question 235
Question: Let f and g be differentiable functions satisfying $ {g}’(a)=2, $
$ g(a)=b $ and $ fog=I $ (identity function). Then $ f’(b) $ is equal to
Options:
A) $ \frac{1}{2} $
B) 2
C) $ \frac{2}{3} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ fog=I\Rightarrow fog(x)=x $ for all x
Therefore $ f’(g(x))g’x=1 $ for all $ x $
Therefore $ f’(g(a))=\frac{1}{g’(a)}=\frac{1}{2}\Rightarrow f’(b)=\frac{1}{2}\ \ \ \ \ \ (\because g(a)=b) $ .
BETA
