Additionally the problem states that f(1) = 1. It is fairly easy to show <---

----> My basic idea is that f(x) = f(x*1) = f(1 + 1 + ... + 1) = f(1) + f(1) + ... + f(1) = 1 + 1 + ... + 1 = x

I feel confident in my reasoning, but given that this was a challenge problem for my Algebra class the simplicity of my proof has me thinking that I left something out. Additionally, the problem gives the condition that f: Q ---> Q, an assumption which I do not appear to have used.

(In the event that my proof is insufficient, please know that I am not at this stage seeking hints. Just need a verification right now.)