Functions
Types of Functions
JEE Main 2022
Grade 12
Question:
The function $f(x) = \frac{x^2 + 2x - 15}{x^2 - 4x + 9}$, $x \in \mathbb{R}$, is:
(1) one-one but not onto
(2) onto but not one-one
(3) both one-one and onto
(4) neither one-one nor onto
Step-by-Step Solution
Key Concept: For one-one: check if $f(x_1) = f(x_2) \Rightarrow x_1 = x_2$. For onto: set $y = f(x)$, rearrange to a quadratic in $x$, and use the discriminant to find the achievable range of $y$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)