Solve this following


Let $f: \mathbb{R}-\{3\} \rightarrow \mathrm{R}-\{1\}$ be defined by

$f(\mathrm{x})=\frac{\mathrm{x}-2}{\mathrm{x}-3}$. Let $\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$ be given as

$g(x)=2 x-3$. Then, the sum of all the values

of $x$ for which $f^{-1}(x)+g^{-1}(x)=\frac{13}{2}$ is equal to



  1. 7

  2. 2

  3. 5

  4. 3

Correct Option: , 3



$\therefore x=\frac{3 y-2}{y-1}$

$\therefore f^{-1}(x)=\frac{3 x-2}{x-1}$

$\& g(x)=y=2 x-3$

$\therefore x=\frac{y+3}{2}$

$\therefore g^{-1}(x)=\frac{x+3}{2}$

$\because f^{-1}(x)+g^{-1}(x)=\frac{13}{2}$

$\therefore x^{2}-5 x+6$

$\therefore$ sum of roots



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