If ƒ(x) = , then the points of discontinuity of the functi…

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If ƒ(x) = , then the points of discontinuity of the function ƒ 3n , (x) is/are where ƒ n = ƒoƒ….oƒ (n times), are -

x = 2

x = {0, 1}

x = –1

Continuous everywhere

Text Solution

Verified by Experts

The correct answer is:

Clearly, x = 1 is a point of discontinuity of the function ƒ(x)

= .

If x ≠ 1, then (ƒoƒ) (x) = ƒ[ƒ(x)]

= ƒ = , which is discontinuous at x = 0.

If x ≠ 0 and x ≠ 1, then

(ƒoƒoƒ) (x) = ƒ[(ƒoƒ) (x)] = ƒ = x,

Which is continuous everywhere.

So, the only points of discontinuity are x = 0 and x = 1.

Hence is the correct answer.

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