JEE Mains · Maths · STD 12 - 1. relation and function
The function \(f: R-\)\(>R,\) \(f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in R\) is
- A both one-one and onto.
- B onto but not one-one.
- C neither one-one nor onto.
- D one-one but not onto.
Answer & Solution
Correct Answer
(C) neither one-one nor onto.
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{(x+5)(x-3)}{x^2-4 x+9}\) Let \(g(x)=x^2-4 x+9\) \( D < 0 \) \( g(x) > 0\) for \(x \in R\) \(\therefore\left[\begin{array}{l}\mathrm{f}(-5)=0 \\ \mathrm{f}(3)=0\end{array}\right.\) So, \(\mathrm{f}(\mathrm{x})\) is many-one. again, \( y x^2-4 x y+9 y=x^2+2 x-15 \)…
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