If f(x)=x 1-x =1 y , then f(y)= - Vidyadip

Question

If $f(x)=\frac{x}{1-x}=\frac{1}{y}$, then $f(y)=$

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Answer

(D) $f(x)=\frac{x}{1-x}=\frac{1}{y}$
$\Rightarrow \quad \frac{1}{y}=\frac{x}{1-x} \Rightarrow y=\frac{1-x}{x}$
then$
\begin{aligned}
f(y) & =\frac{y}{1-y}=\frac{\frac{1-x}{x}}{1-\left(\frac{1-x}{x}\right)}=\frac{\frac{1-x}{x}}{\frac{x-1+x}{x}} \\
& =\frac{1-x}{2 x-1}
\end{aligned}$
hence correct option is

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