Verified Solution • 2025–26 Session moderate

QJEEM25Mac130: JEE Main 2025 Mathematics - Class 12 JEEM25Mac130 Solution: Let denote the greatest integer function, and let m and n…

Let [x][x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x)=[x]+|x-2|,-2< x<3 , is not continuous and not differentiable. Then m+n\mathrm{m}+\mathrm{n} is equal to :

Multiple Choice Options

  • A 6
  • B 9
  • C 8
  • D 7

Step-by-Step Verified Solution

f(x)=[x]+|x−2|−2<x<3

f(x)={−x,−2<x<−1−x+1,−1≤x<0−x+2,0≤x<1−x+3,1≤x<2x,2≤x<3

So f(x)f(x) is not continuous at 4 points and not differentiable at 4 point

So m+n=4+4=8\mathrm{m}+\mathrm{n}=4+4=8

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