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Mathematics Question on Continuity and differentiability

The number of discontinuity of the greatest integer function f(x)=[x], x∈(−72, 100)f\left(x\right)=\left[x\right], \, x\in \left(- \frac{7}{2} , \, 100\right) is equal to

A

104

B

102

C

101

D

103

Answer

103

Explanation

Solution

Given, f(x)=[x], x∈(−3.5, 100)f\left(x\right)=\left[x\right], \, x\in \left(- 3.5 , \, 100\right) As we know greatest integer is discontinuous on integer values. In given interval, the integer values are (−3, −2, −1, 0, …, 99)\left(\right.-3, \, -2, \, -1, \, 0, \, \ldots , \, 99\left.\right) ∴\therefore Total numbers of integers are 103.