If \( f(x)=\log \left[\frac{1+x}{1-x}\right] \), then prove that \[ f\left[\frac{2 x}{1+x^{2}}\r...
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0If \( f(x)=\log \left[\frac{1+x}{1-x}\right] \), then prove that
\[
f\left[\frac{2 x}{1+x^{2}}\right]=2 f(x)
\]
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