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Question

Let f(x)=[x33], where [.] denotes the greatest integer function. Then the number of points in the interval (1,2) where the function is discontinuous, is

A
2
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B
4
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C
6
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D
3
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Solution

The correct option is C 6
f(x)=[x33], x(1,2)
For x(1,2), x33(2,5)
We know that [x] is discontinuous whenever x is an integer.
f(x)=[x33] is discontinuous at all integral points in its range i.e., at six points, corresponding to x33{1,0,1,2,3,4}

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