JEE Main 2024 (Online) 6th April Morning ShiftQuestion 1
The function $f(x)=\frac{x^{2}+2x-15}{x^{2}-4x+9}$, $x\in\mathbb{R}$ is
Functions
Solution
$f(x)=y$ gives $(1-y)x^2+(2+4y)x-15-9y=0$; for $y=0$ it has two real roots $x=-5,3$, so $f$ is not one-one. The discriminant condition restricts $y$ to a bounded set, so $f$ is not onto $\mathbb R$.