I asked this question here. I know it is an "immediate consequence of the theorem", and sometimes we only understand the theorem and don't know how to apply the theorem in an example. So, I wanted to learn how to apply the Fundamental Theorem of Homomorphisms for rings in that example, but I keep getting downvotes. I always try to show what I did as attempts for whatever questions I asked. But, I couldn't do that for that particular post, since I really don't know how to proceed. Is that why I am losing my reputation points? Besides that what exactly is wrong with my question?
At the very least, when you ask for help applying a specific theorem you should include the theorem you want help on in the question. It is okay to copy it verbatim from a textbook (or wherever you have learned that such-and-such is a theorem), but seeing the theorem itself in the question is necessary before anyone can start answering it.
Just giving the name of the theorem is not enough -- different books use the same name for theorems that are slightly different (sometimes equivalent, sometimes not), or use different symbols and letters for the assumptions, and so forth.
One cannot start helping you without knowing exactly what the assumptions and conclusions of the theorem you're looking at is, and what those different assumptions are called in the text you're reading. Otherwise one risks ending up in confusion because what I call $A$ is the thing your book calls $B$ and vice versa.
Concretely, your question seems to fail to explain what $f$ is. It is worded as if $f$ is some map the reader is supposed to know already what is, but since you're not including that information in your question, it is anyone's guess what $im(f)$ is.