Mathematics - Functions Question with Solution | TestHub

$f\left(x\right)=y=\frac{x-2}{x-3}$

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

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

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

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

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

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

$\frac{3x-2}{x-1}+\frac{x+3}{2}=\frac{13}{2}$

$\therefore x^2-5x+6=0$ has roots $x_1,x_2$

$\therefore$ sum of roots $x_1+x_2=5$