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It is impossible for me to finish this work.
It is impossible to me to finish this work.
Are both sentences correct? (Or in the real world are both sentences spoken or written?) Or is the only first sentence correct?
I'm sorry for asking a very basic question, I googled "subject of infinitives" but couldn't get answers.
In my country, in school tests, probably only first sentence is correct.
Unquestionably, OP's first example is "standard/correct" for what I assume is the intended meaning (finishing this work is something that's impossible for me to do myself).
But that's not inherent in the context of constructions involving impossible [preposition] me and an activity expressed using an infinitive form. Consider, for example,...
1: It seems impossible for me to put a man on Mars.
2: It seems impossible to me to put a man on Mars.
Both versions are grammatically valid, but they mean different things.
In #1, for me modifies impossible. Perhaps someone else can put a man on Mars, but apparently I can't.
In #2, to me modifies seems. Perhaps putting a man on Mars seems possible to [some/all] other people.
Note that (probably for semantic reasons), when for me is used in close proximity to a verb like seems, there's a strong tendency for us to interpret them in conjunction. Consider the situation if we slightly reshuffle the word order in #1 above...
1a: For me it seems impossible to put a man on Mars.
1b: It seems for me impossible to put a man on Mars.
I'll admit straight away that #1b is a bit clumsy, but it's not really "ungrammatical". The point is most people would interpret both as semantically equivalent to #2, when for me is moved closer to it seems.
Having said all that, I do not believe all native speakers would always make this semantic distinction in all related contexts. That's to say there's a certain amount of ambiguity that cannot be fully resolved using "rules of grammar".
It often happens in such situations (i.e. - where different prepositions are at least "logically" credible) that if there are also different possible interpretations, idiomatic preference gradually settles on consistently assigning each different interpretation to one particular preposition.
The way this sentence is constructed, the infinitive phrase to finish this work is functioning as an adverb (clarifying is impossible), and you can look at the sentence without that phrase:
It is impossible for (to) me.
It's a rule of English usage that the preposition used in front of me in this case is for, so the first sentence is correct while the second one is incorrect usage.
As @FumbleFingers mentioned, the choice of preposition depends on what the adjective is, so in the case of offensive, the word should be to. (I think this is mostly a reflection of the implied agency in the statements: in the case of impossible, I am the agent, but in the latter case, the offense is happening to me.)
