Question

Let $f: N \rightarrow N$ be defined as $f(n)=\begin{cases}\frac{n+1}{2}, & \text { if } n \text { is odd } \\ \frac{n}{2}, & \text { if } n \text { is even }\end{cases}$ for all $n \in N$. Then $f$ is

• A. injective but not surjective.
• B. surjective but not injective.
• C. both injective as well as surjective.
• D. neither injective nor surjective.

Answer 1

Answer: (B)

As $f(1) = 1 = f (2) $
$ f(3) = 2 = f(4)$
So, f is not injective.
Also, $R_f = N$, so f is surjective.
Hence f is surjective but not injective