1. Injective Function: a function f is said to be injective if and only if, for every element in the codomain, there is at most one element in the domain such that f(x) = y. Codomain Y Domain X “Como mucho”, “al massimo”.

2. Bijective Function: is a function f from a set X to a set Y with the property that, for every element in Y, there is exactly one element in X such that f(x) = y. Codomain Y domain X

3. Surjetive Function: a function f is said to be surjective if its values span its whole codomain; that is, for every element in the codomain, there is at least one element in the domain such that f(x) = y. Codomain Y domain X “por lo menos”, “almeno”. For me, it is not a function in estrictly sense…

4. Bijective Function = Injective Function and Surjective Function Codomain Y domain X No Injective No Surjective

5. Bijective Function = Invertible Function Both are invertibles. To be invertible the function must be decreasing or increasing function. There isn’t a directly connection with second derivative (but the first have to have constant sign).