If the domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a, b)$, then $2 b=$

• A

  $a-1$
• B

  $a$
• C

  $a+1$
• Correct answer
  D

  $a+2$

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