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If `(f(x))^(2)xxf((1-x)/(1+x))=64x AAx in D_(f),` then The value of `f(9//7)` isA. `8(7//9)^(2//3)`B. `4(9//7)^(1//3)`C. `-8(9//7)^(2//3)`D. None of these |
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Answer» Correct Answer - C `(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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