\(\text{ The function }f\left(x\right)=\frac{{x}^{2}+2x-15}{{x}^{2}-4x+9},x\in R\text{ is }\) [JEE Main 2024, 6 Apr (Shi…

\(
\begin{aligned}
&f(x)=\frac{x^2+2x-15}{x^2-4x+9}\\
&f'(x)=\frac{\left(x^2-4x+9\right)(2x+2)-\left(x^2+2x-15\right)(2x-4)}
{\left(x^2-4x+9\right)^2}\\
&f'(x)=\frac{-6x^2+48x-42}{\left(x^2-4x+9\right)^2}
\end{aligned}
\)

So \(f'(x)\) is \(+\)ve and \(-\)ve, hence \(f(x)\) is many-one and into.