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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: 

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a

8

b

7

c

6

d

9

answer is C.

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Detailed 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) is not continuous at 4 points and not differentiable at 4 point
So m + n = 4 + 4 = 8 

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