f(x)={\begin{matrix}|x|+[x];-1\leq x<1 \\ x+|x|;1\leq x<2 \\ |x|+[x];2\leq x\leq 3\end{matrix}
={\begin{matrix}-x-1;-1\leq x<0 \\ x+0;0\leq x<1 \\ 2x;1\leq x<2 \\ x+2;2\leq x<3 \\ 6;x=3 \end{matrix}
At x=0,1,2,3 f changes its definition.
∴ At x=0LHL=−1,RHL=0⇒f is discontinuous at
x=0
x=1LHL=1,RHL=2⇒f is discontinuous at x=1
x=2LHL=RHL=f(2)=4⇒f is continuous at x=2
x=3LHL=5,f(3)=6⇒f is discontinuous at x=1
∴ Points of discontinuity are 0,1,3.