Classify the following function as injection, surjection or bijection: f: Z → Z, defined by

Given f: Z → Z, defined by 

   

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

Injection test:

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

f(x) = f(y)

   

x = y

So, f is an injection.

Surjection test:

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

f(x) = y

   

   

, which is in Z.

So, f is a surjection and f is a bijection