Let f: R -{3} → R -{1} be defined by f(x)=(x-2)/(x-3). Let g: R → R be given as g(x)=2 x-3. Then, the sum of all the values of x for which…

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