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Question:

Let f : [-1, 3] → R be defined as f = |x| + [x] , -1 ≤ x < 1
x+|x| , 1 ≤ x < 2
x + [x] , 2 ≤ x ≤ 3, where [t] denotes the greatest integer less than or equal to t. then, f is discontinuous at:

four or more points

only one point

only two points

only three points

Solution:

Correct option is D. only three points
f(x)=-x-1, -1≤x<0
x, 0≤x<1
2x, 1≤x<2
x+2, 2≤x<3
x+3, x=3
function discontinuous at x=0,1,3