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Abdul Tabeed Rampersad
Asked: 2022-11-10T18:46:07+05:30 In:

If `(f(x))^2+f((1-x)/(1+x))=64 x AA in D_f` then
A. `4x^(2//3)((1+x)/(1-x))^(1//3)`
B. `x^(1//3)((1-x)/(1+x))^(1//3)`
C. `x^(1//3)((1-x)/(1+x))^(1//3)`
D. `x((1+x)/(1-x))^(1//3)`

If `(f(x))^2+f((1-x)/(1+x))=64 x AA in D_f` then
A. `4x^(2//3)((1+x)/(1-x))^(1//3)`
B. `x^(1//3)((1-x)/(1+x))^(1//3)`
C. `x^(1//3)((1-x)/(1+x))^(1//3)`
D. `x((1+x)/(1-x))^(1//3)`
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  1. Correct Answer – A
    `(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)`

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