Check the injectivity and surjectivity of the following functions: f : Z → Z given by f (x) = x 2

Question

Philoid · Accepted Answer

It is given that f : Z → Z given by f (x) = x²

We can see that f(-1) = f(1) = 1, but -1 ≠ 1

⇒ f is not injective.

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

f(x) = x² = -2

⇒ f is not surjective.

Therefore, function f is neither injective nor surjective.