Functions Question 90
Question: If $ f(x)=\frac{x}{1+x} $ , then $ {f^{-1}}(x) $ is equal to
[AMU 1999]
Options:
A) $ \frac{(1+x)}{x} $
B) $ \frac{1}{(1+x)} $
C) $ \frac{(1+x)}{(1-x)} $
D) $ \frac{x}{(1-x)} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\frac{x}{1+x} $ . Let $ y=f(x)\Rightarrow x={f^{-1}}(y) $ \ $ y=\frac{x}{1+x}\Rightarrow y+yx=x $
Þ $ x=\frac{y}{1-y} $
Þ $ {f^{-1}}(y)=\frac{y}{1-y} $
Þ $ {f^{-1}}(x)=\frac{x}{1-x} $ .
BETA
