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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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To prove that \( f\left(\frac{2x}{1+x^2}\right) = 2f(x) \) for the function \( f(x) = \log\left(\frac{1+x}{1-x}\right) \), we will follow these steps: ### Step 1: Substitute into the function We start by substituting \( \frac{2x}{1+x^2} \) into the function \( f \): \[ f\left(\frac{2x}{1+x^2}\right) = \log\left(\frac{1 + \frac{2x}{1+x^2}}{1 - \frac{2x}{1+x^2}}\right) \] ...
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