A) \[\frac{(1+x)}{x}\]
B) \[\frac{1}{(1+x)}\]
C) \[\frac{(1+x)}{(1-x)}\]
D) \[\frac{x}{(1-x)}\]
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 \[{{f}^{-1}}(x)=\frac{x}{1-x}\].
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