Let $f\left(x\right)=\sqrt{\left|x\right|-\left\{x\right\}}$  (where {.} denotes the fractional part of x) and X, Y are its domain and range, respectively). Then

• A

  $x\in \left(-\infty ,\frac{1}{2}\right] \mathrm{and} \mathrm{Y}\in \left[\frac{1}{2},\infty \right)$

• B

  $x\in \left(-\infty ,-\frac{1}{2}\right] \cup \left(0,\infty \right] \mathrm{and} \mathrm{Y}\in \left[\frac{1}{2},\infty \right)$

• C

  $X\in \left(-\infty ,-\frac{1}{2}\right] \cup \left(0,\infty \right] \mathrm{and} \mathrm{Y}\in \left[0,\infty \right)$

• D

  None of these