Mathematics - Continuity - Differentiability Question with Solution | TestHub

We know that the greatest integer function is discontinuous at integral points.

$-5<\frac{x}{2}<5$

$\Rightarrow \left[\frac{x}{2}\right]=-5,-4,-3,-2,-1,0,1,2,3,4$, are the integer values.

At $x=0$, $f\left(0^{+}\right)=f\left(0\right)=f\left(0^{-}\right)=0$, which means that function is continuous at $x=0$.

$\because x\ne -10\Rightarrow \frac{x}{2}\ne -5$

Hence, the function is discontinuous at points $-4,-3,-2,-1,1,2,3,4$

The number of values is $8$ .