Answer :

It is given that

f : N N be defined by



We can observed that:


(by using the definition of f)


Thus, f(1) = f(2), where 1 ≠ 2.


Therefore, f is not one-one.


Now, let us consider a natural number (n) in co domain N.


Case I: When n is odd.


Then, n = 2r +1 for some r ϵ N.


there exist 4r + 1 ϵ N such that f(4r+1) =


Case II: When n is even.


Then, n = 2r for some r ϵ N.


there exist 4r ϵ N such that f(4r) =


Therefore, f is onto.


Function f is not one-one but it is onto.


Thus, Function f is not bijective function.


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