Prepping myself for a graduate abstract course and we are using Dummit and Foote's Text. We are starting on Chapter 1, so I thought it would be a good idea to go over chapter 0. There is a term that I just want clarification on, since it did not come up in my previous modern algebra class or any other text I've seen. 

Suppose we have sets $A$ and $B$, and we define a function on elements of $a$
$$f:A\rightarrow B$$
$$f(a)=b$$

Then $f(A)\subseteq B$ is called the image of $A$ under $f$. Likewise, if $C\subseteq B$, then $f^{-1}(C)\subseteq A$ is called the preimage of $C$ under $f$. 

Then since inverse relations are not necessarily functions, an element of $b\in B$ may have many preimages and these are called fibers. So, as an example, 
let $A=\mathbb{Z}$ and $B=\mathbb{Z\_5}$ and define $f:A\rightarrow B$ such that $f(k)=\bar{k}$, where $k\in\mathbb{Z}$ and $\bar{k}$ is the equivalence class of remainders when dividing elements by $5$. So the fibers of, say $\bar{2}$ are $...-3,2,7,12,... $

It seems to make sense just by definition alone, but I just want to ensure I'm on the right track, as, again, I have never seen this term used before.