CUET · MATHS · PYQ PAPER 2025
The function \(f:[-1,1] \rightarrow \mathbb{R}\) (set of real numbers) given by \(f(x)=\frac{x}{x+3}\) is
- A one-one only
- B onto only
- C both one-one and onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(A) one-one only
Step-by-step Solution
Detailed explanation
Let \(f(x_1) = f(x_2)\): \(\frac{x_1}{x_1+3} = \frac{x_2}{x_2+3}\) \(x_1(x_2+3) = x_2(x_1+3)\) \(x_1x_2 + 3x_1 = x_1x_2 + 3x_2\) \(3x_1 = 3x_2 \implies x_1 = x_2\) Therefore, \(f\) is one-one. Domain: \(x \in [-1,1]\) Codomain: \(\mathbb{R}\)…
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