JEE Mains · Maths · STD 11- 2. Relation and Function
Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined as \(f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3}\). Then \(f\) is :
- A both one-one and onto
- B one-one but not onto
- C onto but not one-one
- D neither one-one nor onto
Answer & Solution
Correct Answer
(D) neither one-one nor onto
Step-by-step Solution
Detailed explanation
Given \(f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3}\) To check for one-one, let \(f(x) = f(y)\) \(\dfrac{2x^2 - 3x + 2}{3x^2 + x + 3} = \dfrac{2y^2 - 3y + 2}{3y^2 + y + 3}\) Cross-multiplying and simplifying, we get: \(11x^2y - 11xy^2 - 11x + 11y = 0\)…
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