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प्रश्न
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
विकल्प
(a) {f(x)}2
(b) {f(x)}3
(c) 2f(x)
(d) 3f(x)
उत्तर
(c) 2f(x)
\[ = \log \left( \frac{\frac{1 + x^2 + 2x}{1 + x^2}}{\frac{1 + x^2 - 2x}{1 + x^2}} \right)\]
\[ = \log \left( \frac{(1 + x )^2}{(1 - x )^2} \right)\]
\[ = 2 \log \left( \frac{1 + x}{1 - x} \right)\]
\[ = 2 (f(x))\]
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