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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`

Text Solution

Verified by Experts

The correct Answer is:
B
`f((2x)/(1+x^2))=ln((1-(2x)/(1+x^2))/(1+(2x)/(1+x^2)))`
`ln.(((x-1)^2)/((x+1)^2))=2ln|(x-1)/(x+1)|`
`=2ln((1-x)/(1+x))=2f(x)`
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