First slide

Algebra of real valued functions

Question

If f(x)=log $(\frac{1 + x}{1 - x})$ then f $(\frac{2 x}{1 + x^{2}})$ isequal to

Easy

A

[f(x)]²
B

[f(x)]³
C

2f(x)
D

3f(x)

Solution

Given f(x)=log $(\frac{1 + x}{1 - x})$
$∴$ f $(\frac{2 x}{1 + x^{2}})$ =log $(\frac{1 + \frac{2 x}{1 + x^{2}}}{1 - \frac{2 x}{1 + x^{2}}})$
=log $(\frac{1 + x^{2} + 2 x}{1 + x^{2} - 2 x})$
=log $[\frac{{(1 + x)}^{2}}{{(1 - x)}^{2}}]$ =log ${(\frac{1 + x}{1 - x})}^{2}$

=2log $(\frac{1 + x}{1 - x})$ =2f(x)

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