Classify the following function as injection, surjection or bijection: f: N → N given by

Given f: N → N, given by

   

Now we have to check for the given function is injection, surjection and bijection condition.

Injection condition:

Let x and y be any two elements in the domain (N), such that f(x) = f(y).

f(x) = f(y)

   

x = y (We do not get 

   

because x and y are in N that is natural numbers)

So, f is an injection.

Surjection condition:

Let y be any element in the co-domain (N), such that f(x) = y for some element x in N (domain).

f(x) = y

   

   

, which may not be in N.

For example, if y =

   

,

x =

   

 is not in N.

So, f is not a surjection.

Also f is not a bijection.