The number of discontinuities of the greatest integer function $\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2},…
The number of discontinuities of the greatest integer function $\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$
104
100
102
103
Solution
$\begin{aligned}
& \mathrm{f}(x)=[x] \\
& x \in\left(\frac{-7}{2}, 100\right) \\
& x \in(-3.5,100)
\end{aligned}$
As we know greatest integer is discontinuous on integer values in given interval, the integer values are $\{-3,-2,-1,0 \ldots 99\}$
$\therefore \quad$ Total number of discontinuities are 103 .