$\text{ If }\left\{\right\}\text{ denotes the fractional part of }x,\text{ the range of the function }f\left(x\right)=\sqrt{{\left\{x\right\}}^2-2\left\{x\right\}}\text{ is }$

$\begin{array}{l}\left\{x^2\right\}-2\left\{x\right\}\ge 0\\ \Rightarrow \left\{x\right\}\left(\right\{x\}-2\}\ge 0\\ \Rightarrow \left\{x\right\}\le 0\text{ or }\left\{x\right\}\ge 2\\ \text{ Second case is not possible. }\\ \text{ Hence }\left\{x\right\}=0,\text{ as }\left\{x\right\}\le [0,1)\\ \text{ Hence range of }f\left(x\right)\text{ contains only one element }0\end{array}$