Let f(x) = [x] + , where [ . ] denotes the greatest intege…

Maths Functions, Limits, Continuity and Differentiability General More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

Let f(x) = [x] + , where [ . ] denotes the greatest integer function. Then

f(x) is continuous on R +

f(x) is continuous on R

f(x) is continuous on R – Ι

discontinuous at x = 1

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

f(x) = [x] +

Curve of y = f(x) =

Method : II y = f(x) can be discontinuous only at x ∈ Ι

so we check continuity only at x = n ∈ Ι

f(n) = [n] +

LHL (x = n) is [n – h] + = (n–1) + 1 = n

RHL (x = n) is [n + h] + = (n+0) = n

f(x) is continous for x ∈ R

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