Question:
Let $\mathrm{f}(\mathrm{x})=\mathrm{x} \cdot\left[\frac{\mathrm{x}}{2}\right]$, for $-10<\mathrm{x}<10$, where $[\mathrm{t}]$ denotes the greatest
integer function. Then the number of points of discontinuity of $f$ is equal to_____.
Solution:
$x \in(-10,10)$
$\frac{x}{2} \in(-5,5) \rightarrow 9$ integers
check continuity at $x=0$
$\left.\begin{array}{l}\mathrm{f}(0)=0 \\ \mathrm{f}\left(0^{+}\right)=0 \\ \mathrm{f}\left(0^{-}\right)=0\end{array}\right\} \quad$ continuous at $\mathrm{x}=0$
function will be distcontinuous when
$\frac{x}{2}=\pm 4, \pm 3, \pm 2, \pm 1$
8 points of discontinuity
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