Question

A mapping $f : N \rightarrow N$, where $N$ is set of natural numbers is defined as $f ( n )=\begin{cases} n ^2, & n =\text { odd } \\ 2 n +1, & n =\text { even }\end{cases}$ for $n \in N$ then $f$ is

• A. surjective but not injective
• B. injective but not surjective
• C. bijective
• D. neither injective nor surjective

Answer 1

Answer: (D)

$\because f (3)= f (4)=9$
$\therefore f \text { is not injective } $
$ f (1)=1, f (2)=5 $
$\therefore f ( x ) \text { can not take the values } 2,3,4 \text { etc. } $
$\therefore f ( x ) \text { is not surjective ] }$