Let f: N arrow N be defined as f(n)= begincases(n+1/2), text if n text is odd (n/2), text if n text is even endcases for all n ∈ N. Then f is

Question

Let f: N arrow N be defined as f(n)= begincases(n+1/2), text if n text is odd (n/2), text if n text is even endcases for all n ∈ N. Then f is (A) injective but not surjective. (B) surjective but not injective. (C) both injective as well as surjective. (D) neither injective nor surjective.

Tardigrade Admin · Accepted Answer

As f(1) = 1 = f (2) f(3) = 2 = f(4) So, f is not injective. Also, Rf = N, so f is surjective. Hence f is surjective but not injective

Q. Let $f : N \to N$ be defined as $f (n) = {\frac{n + 1}{2}, \frac{n}{2}, if n is odd if n is even$ for all $n \in N$ . Then $f$ is

injective but not surjective.

surjective but not injective.

both injective as well as surjective.

neither injective nor surjective.

As $f (1) = 1 = f (2)$
$f (3) = 2 = f (4)$
So, f is not injective.
Also, $R_{f} = N$ , so f is surjective.
Hence f is surjective but not injective

Q. Let f:N→N be defined as f(n)={2n+1​,2n​,​ if n is odd if n is even ​ for all n∈N. Then f is