Question

Let $f(x)=x \cdot\left[\frac{x}{2}\right],$ for $-10<\,x<\,10,$ where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to______.

Answer 1

$x \in(-10,10)$
$\frac{x}{2} \in(-5,5) \rightarrow 9$ integers
check continuity at $x=0$
$f (0)=0\}, f (0^{+})=0\}, f (0^{-}=0\}$ continuous at x = 0
function will be distcontinuous when
$\frac{x}{2}=\pm 4,\pm 3,\pm 2,\pm 1$
8 points of discontinuity