# Let $f(x)=x\cdot\left [ \frac{x}{2} \right ],$ for $-10< x< 10,$ where $\left [ t \right ]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to ______. Option: 1 4 Option: 2 8 Option: 3 2 Option: 4 3

\begin{aligned} &x \in(-10,10)\\ &\frac{x}{2} \in(-5,5) \rightarrow 9 \text { integer }\\ &\text { check continuity at } x=0 \end{aligned}

$\left.\begin{array}{l} \mathrm{f} (0)=0 \\ \mathrm{f} \left(0^{+}\right)=0 \\ \mathrm{f} \left(0^{-}\right)=0 \end{array}\right\} \text { continuous at } \mathrm{x}=0$

the function will be discontinuous when

$\frac{x}{2}=\pm 4,\pm 3,\pm 2,\pm 1$

8 points of discontinuity

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