The range of the real valued function $f(x)=\operatorname{Cos}^{-1}(-x)+\operatorname{Sin}^{-1}(-x)+\operatorname{Cosec}^{-1}(x)$ is

• A

  $\left\{0, \frac{\pi}{2}\right\}$
• B

  $\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]$
• C

  $\left(0, \frac{\pi}{2}\right)$
• Correct answer
  D

  $\{0, \pi\}$

Hence, the correct answer is option: 'D'.