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If `f(x) = log ((1+x)/(1-x))`, where `-1 lt x lt 1` then `f((3x+x^(2))/(1+3x^(2))) - f((2x)/(1+x^(2)))` is equal toA. `[f(x)]^(3)`B. `[f(x)^(2)]`C. `-f(x)`D. `f(x)` |
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Answer» Correct Answer - B Given `f(x)= log ((1+x)/(1-x))` `therefore f((3x + x^(3))/(1+3x^(2))) - f((2x)/(1+x^(2)))` `=log[(1+((3x +x^(3))/(1+3x^(2))))/(1-((3x +x^(2))/(1+3x^(2))))] - log((1+(2x)/(1+x^(2)))/(1-(2x)/(1+x^(2))))` `= log ((1+x)/(1-x))^(3)- log ((1+x)/(1-x))^(2)` ltbr. ` = log ((1+x)/(1-x)) = f(x) ` |
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