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Let f : [-1, 3] → R be defined as f(x) = { |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

1. four or more points
2. only three points
3. only two points
4. only one point

Correct answer: only three points

Solution

The function f is defined piecewise, and discontinuities can occur at the boundaries of the intervals where the definition changes. In this case, the function is discontinuous at the points where the intervals meet, which are x = 1, x = 2, and x = 3, leading to a total of three points of discontinuity.

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