#### Question

If* f*: **R **→ **R **be given by `f(x) = (3 - x^3)^(1/3)` , then *f*o*f*(*x*) is

(A) `1/(x^3)`

(B) *x*^{3}

(C) *x*

(D) (3 − *x*^{3})

#### 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.

Is there an error in this question or solution?

Solution 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) Concept: Composition of Functions and Invertible Function.