The number of points in the interval [2, 4], at which the function f(x) = [ x 2 - x - 1/2 ] , where [·] denotes the greatest integer function, is discontinuous, is

Mathematics · Limits, Continuity and Differentiability

JEE Main 2026 — 2 April, Evening Shift — Question 47

The number of points in the interval [2, 4], at which the function $\mathrm{f(x)} = \left[\mathrm{x}^{2} - \mathrm{x} - \frac{1}{2}\right]$ , where [·] denotes the greatest integer function, is discontinuous, is

Answer: 10

Numerical answer — enter this value.

Step-by-step solution

In $\mathrm{x} \in[2,4]$ , range of $\mathrm{x}^{2}-\mathrm{x}-\frac{1}{2}$ is [1.5, 11.5] $\mathrm{f}(\mathrm{x})$ is discontinuous at points where $\mathrm{x}^{2}-\mathrm{x}-\frac{1}{2}$ becomes integers. ∴ Integral values of $\mathrm{x}^{2}-\mathrm{x}-\frac{1}{2}$ are $2,3,4,5,6,7, 8,9,10,11$ ∴ Number of points where is discontinuous is 10

Answer key and solution verified before publishing.

Practise Limits, Continuity and Differentiability

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 2 April, Evening Shift
Subject: Mathematics
Chapter: Limits, Continuity and Differentiability
Topic: Continuity