A question about ring homomorphisms

[Artusartos]

I attached a page from my textbook, because there was something that I didn't understand.

What I don't understand is in the proof it says let f(x) be...etc. but in the theorem, it says nothing about f(x). In other words, where in the thoerem does it say anything about f(x). Why are they talking about f(x) in the proof?

Thanks in advance

 

[jgens]

Notice that f(x) is just a polynomial in R[x] and the author(s) use it to define the map claimed in the proposition.