If f : R → R is given by f (x) = (3 - x³)^1/3, then fof (x) is:
A. 1/x³ B. x³ C. x D. (3 - x³)^1/3

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B.

According to the given problem,

f : R → R is given by

f (x) = (3 - x³)^1/3

f (x) = (3 - x³)^1/3

Therefore,

fof (x) = f (f (x)) = f ((3 - x³)^1/3)

= [3 - f ((3 - x³)^1/3)³]^1/3

= [3 - (3 - x³)]^1/3

= (x³)^1/3

= x

⇒ fof ( x) = x

The correct answer is C

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.3 Question 13

If f : R → R is given by f (x) = (3 - x³)^1/3, then fof (x) is: A. 1/x³ B. x³ C. x D. (3 - x³)^1/3

Summary:

For the function f : R → R is given by f (x) = (3 - x³)^1/3 , fof ( x) = x. The correct answer is C