A mapping f: N arrow N, where N is set of natural numbers is defined as f ( n )= begincases n 2, n = text odd 2 n +1, n = text even endcases for n ∈ N then f is

Question

A mapping f: N arrow N, where N is set of natural numbers is defined as f ( n )= begincases n 2, n = text odd 2 n +1, n = text even endcases for n ∈ N then f is (A) surjective but not injective (B) injective but not surjective (C) bijective (D) neither injective nor surjective

Tardigrade Admin · Accepted Answer

∵ f (3)= f (4)=9 ∴ f text is not injective f (1)=1, f (2)=5 ∴ f ( x ) text can not take the values 2,3,4 text etc. ∴ f ( x ) text is not surjective ]

Q. A mapping $f : N \to N$ , where $N$ is set of natural numbers is defined as $f (n) = {n^{2}, 2 n + 1, n = odd n = even$ for $n \in N$ then $f$ is

surjective but not injective

injective but not surjective

bijective

neither injective nor surjective

$∵ f (3) = f (4) = 9$
$∴ f is not injective$
$f (1) = 1, f (2) = 5$
$∴ f (x) can not take the values 2, 3, 4 etc.$
$∴ f (x) is not surjective ]$

Q. A mapping f:N→N, where N is set of natural numbers is defined as f(n)={n2,2n+1,​n= odd n= even ​ for n∈N then f is