Let [·] denote the greatest integer function, and let f(x)= min {√ 2 x, x^2}. Let S ={x ∈(-2,2).: the function g (x)=|x|[x^2] is discontinuous at.x}.…

Let $\displaystyle [\cdot]$ denote the greatest integer function, and let $\displaystyle f(x)=\min \left\{\sqrt{2} x, x^2\right\}$. Let $\displaystyle \mathrm{S}=\left\{x \in(-2,2)\right.$ : the function $\displaystyle \mathrm{g}(x)=|x|\left[x^2\right]$ is discontinuous at $\displaystyle \left.x\right\}$. Then $\displaystyle \sum_{x \in \mathrm{~S}} f(x)$ equals