If `(f(x))^(2)xxf((1-x)/(1+x))=64x AAx in D_(f),` then
The value of `f(9//7)` is

Options

A. `8(7//9)^(2//3)`
B. `4(9//7)^(1//3)`
C. `-8(9//7)^(2//3)`
D. None of these

Answer

C

Explanation

`(f(x))^(2)f((1-x)/(1+x))=64x " (1)" `
Putting `(1-x)/(1+x)=y or x=(1-y)/(1+y),` We get
`{f((1-y)/(1+y))}^(2)*f(y)=64((1-y)/(1+y))`
` or f(x)*{f((1-x)/(1+x))}^(2)=64((1-x)/(1+x)) " (2)" `
Squaring (1) and dividing by (2),
`(f(x)^(4){f((1-x)/(1+x))}^(2))/(f(x){f((1-x)/(1+x))}^(2))=((64x)^(2))/(64((1-x)/(1+x)))`
`or {f(x)}^(3)=64x^(2)((1+x)/(1-x))`
` or f(x)=4x^(2//3)((1+x)/(1-x))^(1//3)`
` :. f(9//7)= -4(9//7)^(2//3)(2)`