Let f:[-1,3] IR be defined as f(x)= cases |x|+[x], & -1 x<1 x+|x|, & 1 x<2 x+[x], & 2 x<3 cases where [t] denotes the greatest integer function. Then f is discontinuous at

MHT CET 2024 Mathematics question

Let be defined as

f(x)=

where denotes the greatest integer function. Then is discontinuous at

(A)only two pointsCorrect
(B)only three points
(C)four or more points
(D)only one points

Answer: (A)

Solution

Each piece is continuous inside its interval except where jumps, i.e. at integers, so test . At : left limit , while and the right limit is , so is discontinuous at 0. At : left limit , but , so discontinuous at 1. At :

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Question ID VK-098961