The function f(x) = [x] 2 − − [x 2 ] (where [y] is the grea…

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The function f(x) = [x] 2 − − [x 2 ] (where [y] is the greatest integer less than or equal to y), is discontinuous at

All integers

All ingtegers except 0

All integers except

Text Solution

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The correct answer is:

We have f(x) = [x] 2 – [x] 2

At x = 0, L.H.L. =

R.H.L. =

∴ ∴ L.H.L ≠ ≠ R.H.L. ∴ ∴ f(x) is not continuous at x = 0.

At x = 1, L.H.L.,

R.H.L. =

f(1) = [1] 2 − − [1] 2 = 1 − − 1 = 0

∴ ∴ L.H.L. = R.H.L. = f(1) ∴ ∴ f(x) is continuous at x = 1.

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