We have made it to function proofs in my class. I really have a hard time understanding proofs at all. Can someone explain to me how these couple examples:
These are 2 of many questions from my homework, and I have no idea how to do them.
Let f : Z x Z --> Z state whether the following function is onto or not, then prove or disprove.
f(m, n) = m2 + n4
I understand that the domain is Z x Z and the codomain is Z, And I know that to be onto the function, if y element Y implies there is an x element X such that f(x)=y, I just don't understand how you prove it.
Let f : Z --> Z state whether the following function is one to one or not, then prove or disprove.
f(n) = n2 + 1
Thank for everyone who helps me learn how to prove these, I really won't be able to understand the rest of my work without you're explanations.