Question

A function f from the set of natural numbers to integers defined by $f(n) = \left{ \begin{matrix} \frac{n - 1}{2},\text{when}n\text{isodd} \

• \frac{n}{2},\text{when}n\text{iseven} \end{matrix} \right.\ $, is

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

Answer 1

Answer: (C)

One-one and onto both

Answer 2

$f:N \rightarrow I$

$f(1) = 0,f(2) = - 1,f(3) = 1,f(4) = - 2,f(5) = 2$ and $f(6) = - 3$ so on.

In this type of function every element of set A has unique image in set B and there is no element left in set B. Hence f is one-one and onto function.