Question

A function \( f \) from the set of natural numbers to integers defined by \[ f(n) = \begin{cases} \frac{n-1}{2}, & \text{when } n \text{ is odd} -\frac{n}{2}, & \text{when } n \text{ is even} \end{cases} \] is

• A. neither one-one nor onto
• B. one-one but not onto
• C. onto but not one-one
• D. one-one and onto

Hint:

Split domain into cases (odd/even) to analyze injectivity and surjectivity clearly.

Answer 1

The Correct Option is D