The domain of $f\left(x\right)=\sqrt{2{\left\{x\right\}}^2-3\left\{x\right\}+1},$ where {.} denotes the fractional part in [ -1, 1], is

• A

  $\left[-1,1\right]~\left(\frac{1}{2},1\right)$

• B

  $\left[-1,-\frac{1}{2}\right]\cup \left[0,\frac{1}{2}\right]\cup \left\{1\right\}$

• C

  $\left[-1,\frac{1}{2}\right]$

• D

  $\left[-\frac{1}{2},1\right]$