Let f(x) = x . [x/2], for -10 < x < 10, where [t] denotes the greatest integer function.

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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