QJEEM24Ma9e1a: JEE Main 2024 Mathematics - Class 11 JEEM24Ma9e1a Solution: The function is

The function $f(x)=\frac{x^2+2x-15}{x^2-4x+9}, x \in \mathbb{R}$ can be simplified to $f(x)=\frac{(x-3)(x+5)}{x^2-4x+9}$ .

For $x=3$ and $x=-5$ , $f(x)$ equals 0. Therefore, $f(x)$ is not one-one as it yields the same output for different input values.

The range of $f(x)$ is $[-2, 1.6]$ , indicating that $f(x)$ does not cover all possible real values. Consequently, $f(x)$ is not onto.

Thus, the function is neither one-one nor onto.