A good starting point therefore would be to try to understand some things that are not possible in imperative languages but possible in functional languages.
If you're talking about computability, there is of course nothing that is possible in functional but not imperative programming (or vice versa).
The point of different programming paradigms isn't to make things possible that weren't possible before, it's to make things easy that were hard before.
Functional programming aims to let you more easily write programs that are concise, bug-free and parallelizable.