Let f: N arrow N defined by f(n)= begincases(n+1/2) text if n text is odd (n/2) text if n text is even endcases, then f is

Question

Let f: N arrow N defined by f(n)= begincases(n+1/2) text if n text is odd (n/2) text if n text is even endcases, then f is (A) Onto but not one-one (B) one-one and onto (C) Neither one-one nor onto (D) one-one but not onto

Tardigrade Admin · Accepted Answer

( m +1/2), m is odd f (2 n -1)= n (m/2)=n, n is even f (2 n )= n ∀ n ∈ N There exists m (=2 m -1 or 2 n ), f ( m )= n f is onto

Q. Let $f : N \to N$ defined by $f (n) = {\frac{n + 1}{2} \frac{n}{2} if n is odd if n is even$ , then $f$ is

Onto but not one-one

one-one and onto

Neither one-one nor onto

one-one but not onto

$\frac{m + 1}{2}, m$ is odd $f (2 n - 1) = n$
$\frac{m}{2} = n, n$ is even $f (2 n) = n$
$\forall n \in N$ There exists $m (= 2 m - 1$ or $2 n), f (m) = n$ $f$ is onto

Q. Let f:N→N defined by f(n)={2n+1​2n​​ if n is odd if n is even ​, then f is