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

Options

A. `[0,oo)`
B. `R-{1}`
C. `(-oo,oo)`
D. None of these

Answer

B

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)`