Define F : Z → Z by the rule F(n) = 2 -3n, for all integers n

Question

I am not sure how to go about solving this problem. Can somebody tell me how to define $F : Z \to Z$ by the rule $F(n) = 2 -3n$, for all integers $n$ ?

I am not sure where to even start or what is meant by the question. The assignment continues:

i) Is $F$ one-to-one? (Prove or give a counterexample.)

ii) Is $F$ onto? (Prove or give a counterexample.)

Any help that points me in the right direction to go about solving such a problem is greatly appreciated.

Answer 1

i) $F$ is one to one. We want to show from $F(a)=F(b)$ we can conclude $a=b$. I will let you see if you can conclude this part. ii) F is not surjective. Counterexample: 0 is an integer but $2-3n \neq 0$ for any integer $n$. Summary: Basically for i) for one-to-one: we want to show there is no element in the codomain that gets hit more than once. ii) for onto: for this we want to show every element of the codomain gets hit at least once