write, in proper mathematical terminology, what it means for a?

Question

function f: A -> B not to be injective, and not to be surjective

Answer 1

For one thing, it would be true that, for at least one value a and b that f(a)=f(b) even though a is not equal to b. To not be surjective, there would exist a value a such that f(x) is not equal to a for any value of x in the domain of the function f.

Answer 2

not bijective.

A bijective function is injective and surjective, so the contrapositive is true: a non-injective and non-surjective function implies the function is not bijective.