Let $\mathrm{f}(x)=\left\{\begin{array}{lc}3 x, & x \lt 0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\ 5, & x \gt 2,\end{array}\right.$
where [.] denotes 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 __________

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Aicharya · Accepted Answer

$f(x)=\left\{\begin{array}{ccc}3 x & ; & x 2\end{array}\right.$ $f(x)=\left\{\begin{array}{ccc}3 x & ; & x 2\end{array}\right.$ Not continuous at $\mathrm{x} \in\{1,2\} \Rightarrow \alpha=2$ Not diff. at $x \in\{0,1,2\} \Rightarrow \beta=3$ $\alpha+\beta=5$

Let $\mathrm{f}(x)=\left\{\begin{array}{lc}3 x, & x \lt 0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\…

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