JEE Main 2021 (Online) 18th March Evening ShiftQuestion 1
Let $f:\mathbf{R}-\{3\}\to\mathbf{R}-\{1\}$ be defined by $f(x)=\frac{x-2}{x-3}$. Let $g:\mathbf{R}\to\mathbf{R}$ be given as $g(x)=2x-3$. Then, the sum of all the values of $x$ for which $f^{-1}(x)+g^{-1}(x)=\frac{13}{2}$ is equal to :
Functions
Solution
$f^{-1}(x)=\frac{3x-2}{x-1}$, $g^{-1}(x)=\frac{x+3}2$. Then $\frac{3x-2}{x-1}=\frac{10-x}2$ gives $x^2-5x+6=0$, $x=2,3$, sum $5$.