COMEDK · Maths · 24. Functions
A function \(f\) from the set of natural numbers to integers defined by \(f(n)=\left\{\begin{array}{l}\dfrac{n-1}{2}, \quad \text { when } n \text { is odd } \\ -\dfrac{n}{2}, \quad \text { when } n \text { is even }\end{array} \quad\right.\) is
- A onto but not one-one
- B one-one but not onto
- C neither one-one nor onto
- D one-one and onto
Answer & Solution
Correct Answer
(D) one-one and onto
Step-by-step Solution
Detailed explanation
The function \(f: \mathbb{N} \rightarrow \mathbb{Z}\) is defined as \(f(n) = \dfrac{n-1}{2}\) if \(n\) is odd and \(f(n) = -\dfrac{n}{2}\) if \(n\) is even. To check for one-one, consider two distinct natural numbers \(n_1\) and \(n_2\). If \(n_1\) is odd and \(n_2\) is even,…
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