• 072920 77839
  • info@smartachievers.in
Menu
Back
  • JEE ADVANCE
  • JEE MAIN
  • NEET
  • BITSAT
  • CBSE BOARD
  • UP BOARD
  • CUET
JEE ADVANCE
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
JEE MAIN
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
NEET
  • CLASS XI - XII
  • CRASH COURSE
BITSAT
  • CLASS XI - XII
CBSE BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
  • CLASS VI
  • CLASS VII
  • CLASS VIII
UP BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
CUET
  • CRASH COURSE
Courses


Solution


Q.

Let [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 is equal to :          [2025]
1 7  
2 8  
3 6  
4 9  

Ans.

(2)

Given : f(x)=[x]+|x–2|,–2<x<3

The function can also be written as follows:

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

Here, function f(x) is not continuous at x = –1, 0, 1 and 2.

Hence, function f(x) is not differentiable at x = –1, 0, 1 and 2.

So, we have m = n = 4.

∴   m + n = 4 + 4 = 8.