The domain of the derivative of the function $f(x)=\operatorname{Cos}^{-1}(2 x-5)-\operatorname{Sin}^{-1}(x-2)$ is

• A

  $[2,3]$
• B

  $(-\infty, 2] \cup[3, \infty)$
• C

  $(-\infty, 2) \cup(3, \infty)$
• Correct answer
  D

  $(2,3)$

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