Mathematics Question from JEE Main 2025 · 28 January, Shift 1

Let $f(x)$ be defined as follows:

$$f(x) = \begin{cases} 3x, & \text{if } x < 0\\ \min(1+x+\lfloor x \rfloor, 2+x\lfloor x \rfloor), & \text{if } 0 \leq x \leq 2\\ 5, & \text{if } x > 2 \end{cases}$$

where $\lfloor . \rfloor$ denotes the greatest integer function. If $\alpha$ and $\beta$ are the number of points, where $f$ is not continuous and is not differentiable, respectively, then $\alpha + \beta$ equals: