Question

Let $f: N \rightarrow N$ defined by $f(n)=\begin{cases}\frac{n+1}{2} & \text { if } n \text { is odd } \\ \frac{n}{2} & \text { if } n \text { is even }\end{cases}$, then $f$ is

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

Answer 1

Answer: (A)

$\frac{ m +1}{2}, m$ is odd $f (2 n -1)= n$
$\frac{m}{2}=n, n$ is even $f (2 n )= n$
$\forall n \in N$ There exists $m (=2 m -1$ or $2 n ), f ( m )= n$ $f$ is onto