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Question
Let f(x)=[x3ā3], where [.] denotes the greatest integer function. Then the number of points in the interval (1,2) where the function is discontinuous, is
Let f(x)=[x3ā3], where [.] denotes the greatest integer function. Then the number of points in the interval (1,2) where the function is discontinuous, is
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Solution
The correct option is C 6
f(x)=[x3−3], x∈(1,2)
For x∈(1,2), x3−3∈(−2,5)
We know that [x] is discontinuous whenever x is an integer.
∴f(x)=[x3−3] is discontinuous at all integral points in its range i.e., at six points, corresponding to x3−3∈{−1,0,1,2,3,4}
f(x)=[x3−3], x∈(1,2)
For x∈(1,2), x3−3∈(−2,5)
We know that [x] is discontinuous whenever x is an integer.
∴f(x)=[x3−3] is discontinuous at all integral points in its range i.e., at six points, corresponding to x3−3∈{−1,0,1,2,3,4}
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