Check the injectivity and surjectivity of the following functions:

f : Z Z given by f (x) = x3

It is given that f : Z Z given by f (x) = x3

We can see that for x, y ϵ N,


f(x) = f(y)


x3 = y3


x = y


f is injective.


Now, let 2 ϵ Z. But, we can see that there does not exists any x in Z such that


f(x) = x3 = 2


f is not surjective.


Therefore, function f is injective but not surjective.


4