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# Solve the following

Question:

If $f(x)=\log _{e}\left(\frac{1-x}{1+x}\right),|x|<1$, then $f\left(\frac{2 x}{1+x^{2}}\right)$ is equal to :

1. $2 f(\mathrm{x})$

2. $2 f\left(x^{2}\right)$

3. $(f(x))^{2}$

4. $-2 f(x)$

Correct Option: 1

Solution: