Let $f:R-\left\{3\right\}\to R-\left\{1\right\}$ be defined by $f\left(x\right)=\frac{x-2}{x-3}$. Let $g : R\to R$ be given as $g\left(x\right)=2x-3$. Then, the sum of all the values of $x$ for which $f^{-1}\left(x\right)+g^{-1}\left(x\right)=\frac{13}{2}$ is equal to

• A

  $7$
• B

  $2$
• Correct answer
  C

  $5$
• D

  $3$

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