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If f(x)=log[(1+x)/(1-x)], then prove tha...

If `f(x)=log[(1+x)/(1-x)],` then prove that `f[(2x)/(1+x^2)]=2f(x)dot`

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`f(x)=log[(1+x)/(1-x)]`
or `f((2x)/(1+x^(2)))=log[(1+(2x)/(1+x^(2)))/(1-(2x)/(1+x^(2)))]=log[(x^(2)+1+2x)/(x^(2)+1-2x)]`
`=log[(1+x)/(1-x)]^(2)=2 log [(1+x)/(1-x)]=2f(x)`
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