Let $\mathrm{f}(x)=x\left[\frac{x}{2}\right]$, for $-10 \lt x \lt 10$, where $[\mathrm{t}]$ denotes the…
Let $\mathrm{f}(x)=x\left[\frac{x}{2}\right]$, for $-10 \lt x \lt 10$, where $[\mathrm{t}]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to
10
9
6
8
Solution
$\begin{aligned}
& -10 \lt x \lt 10 \\
& \Rightarrow-5 \lt \frac{x}{2} \lt 5 \\
& \Rightarrow \frac{x}{2}=0, \pm 1, \pm 2, \pm 3, \pm 4
\end{aligned}$ But $\mathrm{f}(x)$ is continuous at $x=0$.
$\therefore \quad$ There are 8 points of discontinuity i.e. $-4,-3$, $-2,-1,1,2,3,4$.