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)

Answer 1

`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.