A) \[x\]
B) \[\left( \frac{x}{1-x} \right)\]
C) \[\frac{1-x}{x}\]
D) \[\frac{1}{x}\]
E) \[\left( \frac{x}{1+x} \right)\]
Correct Answer: B
Solution :
\[f(x)=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+....\infty ,|x|<1\] \[f(x)=\frac{x}{1-(-x)}=\frac{x}{1+x}\] \[\Rightarrow \] \[f(x)=y=\frac{x}{1+x}\] \[\Rightarrow \] \[y(1+x)=x\] \[\Rightarrow \] \[x=\frac{y}{1-y}\] \[\therefore \] \[{{f}^{-1}}(x)=\frac{x}{1-x}\]You need to login to perform this action.
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