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# 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) - CBSE (Science) Class 12 - Mathematics

ConceptComposition of Functions and Invertible Function

#### Question

If f→ 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

fR → 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

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.