Is there an infinite field $k$ together with a polynomial $f \in k[x]$ such that the associated map $f \colon k \to k$ is not surjective but misses only finitely many elements in $ …

As a starting note, I would like to say that I haven't (yet) taken courses in Set Theory, so some higher-level notation may be lost on me (and I may not write everything convention …

Here is my first question, I'm preparing for the Analysis 1 exam and I found something that bothers me (not the first that shakes me I have to admit). If this is not a suitable que …