Differentiation Question 190
Question: If $ f(x)=\frac{1}{1-x} $ , then the derivative of the composite function $ f
[f{f(x)}] $ is equal to [Orissa JEE 2003]
Options:
A) 0
B) $ \frac{1}{2} $
C) 1
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\frac{1}{1-x} $
Therefore $ f{f(x)}=\frac{1-x}{-x} $
$ \Rightarrow $ $ f[f{f(x)}]=\frac{-x}{-x-1+x}=x $
$ \therefore $ Derivative of $ f[f{f(x)}]=1 $ .
BETA
