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Question
If f: R → R be given by `f(x) = (3 - x^3)^(1/3)`, then fof(x) is ______.
Options
`1/(x^3)`
x3
x
(3 – x3)
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Solution
x
Explanation:
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
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