JEE Main 2023MathematicsContinuity and DifferentiabilityMediumNumerical

JEE Main 2023 — Continuity and Differentiability Question with Solution

JEE Main 2023 (12 Apr Shift 1)

Question

Let x be the greatest integer ≤x. Then the number of points in the interval (–2, 1) where the function fx=x+x-x is discontinuous, is _____.

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given,

fx=x+x-x

x-x≥0⇒x∈R

Now using the property of greatest integer function and simplifying the function we get,

fx=2+x+2,  -2<x<-11+x+1,   -1≤x<0x,       0≤x<1 

Now plotting the diagram we get,

Now from the diagram we can say that, fx is discontinuous at two points x=–1, 0.

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About this question

This is a previous-year question from JEE Main 2023, covering the Continuity and Differentiability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.