JEE Main 2023MathematicsContinuity and DifferentiabilityHardNumerical

JEE Main 2023 — Continuity and Differentiability Question with Solution

JEE Main 2023 (10 Apr Shift 1)

Question

Let f:-2, 2→ℝ be defined by fx=xx,-2<x<0x-1x,0≤x<2 where x denotes the greatest integer function. If m and n respectively are the number of points in –2, 2 at which y=fx is not continuous and not differentiable, then m+n is equal to ________.  

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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

Given,

f:-2, 2→ℝ be defined by fx=xx,-2<x<0x-1x,0≤x<2

⇒fx=-2x, -2<x<-1-x, -1≤x<00, 0<x<1x-1, 1≤x<2

Now plotting the diagram of the above function we get,

Now from above diagram we can say that, y=fx is same as y=fx

Hence, the function is not continuous at one point and non differentiable at three points, so m=1, n=3

Hence, m+n=4

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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.