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Question
If f: R → R be given by `f(x) = (3 - x^3)^(1/3)` , then fof(x) is
(A) `1/(x^3)`
(B) x3
(C) x
(D) (3 − x3)
Solution
`f: R → R is given as `f(x) = (3 - x^3)^(1/3)
`f(x) = (3 - x^3)^(1/3)`
`:. fof(x) = f(f(x)) = f((3-x^3)^(1/3)) = [3 - ((3 - x^3)^(1/3))^3]^(1/3)`
`= [3 - (3 - x^3)]^(1/3) = (x^3)^(1/3) = x`
:. fof(x) = x
The correct answer is C.
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