A function f from the set of natural numbers to integers is defined by n when n is odd f(n) 3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

Explanation

Given that, `f(n)={l}frac{n-1}{2}, text { when } n text { is odd } -frac{n}{2}, text { when } n text { is even }`


and `f: N -> l`, where `N` is the set of natural numbers and `/` is the set of integers.


Let `x, y in N` and both are even.


Then, `f(x)=f(y) Rightarrow-frac{x}{2}=-frac{y}{2} Rightarrow x=y`


Again, `x, y in N` and both are odd.


Then, `f(x)=f(y) Rightarrow frac{x-1}{2}=frac{y-1}{2} Rightarrow x=y`