Question

Let f : $N\to N$ defined by $f\left(n\right)=\{\begin{array}{cc}\frac{n+1}{2}& \text{if}n\text{is odd}\\ \frac{n}{2}& \text{if}n\text{is even}\end{array}$
then $f$ is.

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

Answer 1

The correct option is A Many-one and onto

By substituting values of $n$, the elements in the range of function are,

$\{1,2,3,4,5,6,...............\}$, i.e. set of all natural number

So the range and co-domain are same, ergo function is onto.

Also $f\left(1\right)=f\left(2\right)$, so the function is many one.

Hence the given function is many-one and onto