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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

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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

The correct answer is C.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 13 | Page no. 19
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.
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