Consider the function $f\left(x\right)={\cos }^{-1}\left(\left[3^x\right]\right)+{\sin }^{-1}\left(\left[3^x\right]-1\right)$, then (where, $\left[\cdot \right]$ represents the greatest integer part of $x$)

• A

  the domain of $f\left(x\right)$ is $x\in \left(-\infty , 0\right]$
• Correct answer
  B

  the range of $f\left(x\right)$ is singleton
• C

  $f\left(x\right)$ is an even function
• D

  $f\left(x\right)$ is an odd function

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