Functions Question 526
Question: If $ f(x)=x-x^{2}+x^{3}-x^{4}+…to $ $ \infty $ for $ | x |<1, $ then $ {f^{-1}}(x)= $
Options:
A) $ \frac{x}{1+x} $
B) $ \frac{x}{1-x} $
C) $ \frac{1-x}{x} $
D) $ \frac{1}{x} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given $ f(x)=x-x^{2}+x^{3}-x^{4}+…to\infty $
$ \Rightarrow y=\frac{x}{1+x} $ (Infinite G.P.)
$ \Rightarrow y+xy=x\Rightarrow y=x(1-y) $
$ \Rightarrow x=\frac{y}{1-y} $
$ \Rightarrow {f^{-1}}(y)=\frac{y}{1-y}\Rightarrow f^{1}(x)=\frac{x}{1-x} $
BETA
