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If $f(x) = \log_e\left(\frac{1-x}{1+x}\right)$, $|x| < 1$, then $f\left(\frac{2x}{1+x^2}\right)$ is equal to:
(1) $2f(x)$
(2) $2f(x^2)$
(3) $(f(x))^2$
(4) $-2f(x)$
Type: MCQ
$f\left(\frac{2x}{1+x^2}\right) = \log\left(\frac{(1-x)^2}{(1+x)^2}\right) = 2\log\left(\frac{1-x}{1+x}\right) = 2f(x)$
BETA
