\(\text{ The function }f\left(x\right)=\frac{{x}^{2}+2x-15}{{x}^{2}-4x+9},x\in R\text{ is }\) [JEE Main 2024, 6 Apr (Shi…
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PYQ\(\text{ The function }f\left(x\right)=\frac{{x}^{2}+2x-15}{{x}^{2}-4x+9},x\in R\text{ is }\)
[JEE Main 2024, 6 Apr (Shift 1)]
✓ Correct answer: b)
neither one-one nor onto.
Explanation
\(\begin{aligned}&f(x)=\frac{x^2+2x-15}{x^2-4x+9}\\&f'(x)=\frac{\left(x^2-4x+9\right)(2x+2)-\left(x^2+2x-15\right)(2x-4)}{\left(x^2-4x+9\right)^2}\\&f'(x)=\frac{-6x^2+48x-42}{\left(x^2-4x+9\right)^2}\end{aligned}\)
So \(f'(x)\) is \(+\)ve and \(-\)ve, hence \(f(x)\) is many-one and into.
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