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 to

Options

A. `[f(x)]^(3)`
B. `[f(x)^(2)]`
C. `-f(x)`
D. `f(x)`

Answer

B

Explanation

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) `