Question

Let $[ t ]$ denote the greatest integer $\leq t$. The number of points where the function
$f ( x )=[ x ]\left| x ^{2}-1\right|+\sin \left(\frac{\pi}{[ x ]+3}\right)-[ x +1], x \in(-2,2)$ is not continuous is

Answer 1

$f(x)=[x]\left|x^{2}-1\right|+\sin \frac{\pi}{[x+3]}-[x+1]$
$f(x)=\begin{cases}3-2 x^{2}, & -2< x< -1 \\ x^{2}, & -1 \leq x< 0 \\ \frac{\sqrt{3}}{2}+1 & 0 \leq x<1 \\ x^{2}+1+\frac{1}{\sqrt{2}}, & 1 \leq x< 2\end{cases}$
discontinuous at $x=0,1$