CUET · MATHS · PYQ PAPER 2025
Let \(N\) be set of natural numbers, then the function \(f : N \rightarrow N\), defined by
\(f(n)=\left\{\begin{array}{ll}\frac{n+1}{2} & ,\text { if } n \text { is odd } \\ \frac{n}{2} & , \text { if } n \text { is even }\end{array}\right.\) is
- A injective but not surjective
- B surjective but not injective
- C bijective
- D neither injective nor surjective
Answer & Solution
Correct Answer
(B) surjective but not injective
Step-by-step Solution
Detailed explanation
\(f(1) = \frac{1+1}{2} = 1\) \(f(2) = \frac{2}{2} = 1\) \(f(1)=f(2)\) but \(1 \neq 2 \implies\) Not injective. For any \(y \in N\), let \(n=2y\). \(n \in N\) and is even. \(f(n) = f(2y) = \frac{2y}{2} = y\). Therefore, surjective.
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