Question

Is x implies x^2 an injection function?

To my knowledge:
Injection means injective but not surjective.
Surjection means surjective but not injective.
So this function is not surjective because each element of the codomain is not mapped to at least one element in the domain.
And it's injective because each element in domain is mapped to at most 1 element in codomain.

Is this correct?

Answer 1

Saying a function is injective tells you nothing as to whether the function is surjective.

An injection is just an injective function (which may or may not be surjective).

Also, \(f(x)=x^2\) is not injective for certain parts of its domain. For example, \(f(-1)=f(1)=1\).