JEE Main 2024 — Functions Question with Solution

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.