Question

If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\]  is equal to

 

 

पर्याय

• (a) {f(x)}²

• (b) {f(x)}³

• (c) 2f(x)

• (d) 3f(x)

   

Answer 1

(c) 2f(x) 

\[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\]

\[\text{ Then } , f\left( \frac{2x}{1 + x^2} \right) = \log \left( \frac{1 + \frac{2x}{1 + x^2}}{1 - \frac{2x}{1 + x^2}} \right)\]
\[ = \log \left( \frac{\frac{1 + x^2 + 2x}{1 + x^2}}{\frac{1 + x^2 - 2x}{1 + x^2}} \right)\]
\[ = \log \left( \frac{(1 + x )^2}{(1 - x )^2} \right)\]
\[ = 2 \log \left( \frac{1 + x}{1 - x} \right)\]
\[ = 2 (f(x))\]