Let [x] denote the greatest integer function and f(x)= max {1+x+[x], 2+x, x+2[x]}, 0 ≤ x ≤ 2. Let m be the number of points in [0,2], where f is not…

Let $\displaystyle [x]$ denote the greatest integer function and $\displaystyle f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2$. Let $\displaystyle m$ be the number of points in $\displaystyle [0,2]$, where $\displaystyle f$ is not continuous and $\displaystyle n$ be the number of points in $\displaystyle (0,2)$, where $\displaystyle f$ is not differentiable. Then $\displaystyle (m+n)^2+2$ is equal to