Mathematics - Continuity - Differentiability Question with Solution | TestHub

Check for $\left[\frac{x^2}{2}\right]$ and $[\sqrt{x}]$ becomes integers.
$\{0,1,\sqrt{2},2,\sqrt{6},\sqrt{8},\sqrt{10},\sqrt{12},\sqrt{14},4\}$
Continuous at $0^{+}$, continuous at $4^{-}$ $\left[\frac{x^2}{2}\right]=[\sqrt{x}]$, occurs at $x=\sqrt{2}$
$\Rightarrow$ Not continuous