If $f(x)=2+\left|\operatorname{Sin}^{-1} x\right|$ and $A=\left\{x \in R / f^1(x)\right.$ exists $\}$, then $A=$

• A

  $\{0\}$
• B

  $[-1,1]$
• C

  $(-\infty,-1) \cup(1, \infty)$
• Correct answer
  D

  $(-1,0) \cup(0,1)$

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