CUET · MATHS · PYQ PAPER 2025
A relation \(f: N \rightarrow N\) be defined by \(f(x)=x^2, x \in N\) (Set of Natural numbers), Then \(f(x)\) is
- A neither injective nor surjective
- B injective only
- C surjective only
- D bijective
Answer & Solution
Correct Answer
(B) injective only
Step-by-step Solution
Detailed explanation
1. Injectivity: Assume \(f(x_1) = f(x_2)\). \(x_1^2 = x_2^2\) \(x_1 = x_2\) (since \(x_1, x_2 \in N\)). Hence, \(f\) is injective. 2. Surjectivity: For \(y=2 \in N\) (codomain), there is no \(x \in N\) such that \(x^2=2\). Thus, \(f\) is not surjective. The function is injective…
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