If a prophecy declared before Oedipus is born that he will kill his father and marry his mother in Oedipus Rex, is his fate predetermined?
The very good enotes study guide on this tragedy includes the following comment under the theme "choice and consequences":
Another theme in the play is the distinction between the truthfulness of oracles and prophecies of the gods (fate), as opposed to man's ability to influence his life's trajectory through his own actions (free will or self-determinism). ... Oedipus Rex emphasizes the eventual and tragic triumph of the former over the latter. Despite his best efforts to be a good and wise king and to substantiate his claims about the evil machinations of Creon and Teiresias, fate works against him and finally shows that he was wrong to believe in a conspiracy.
I would add that it's not just Oedipus' fate that seems predetermined. The fate of his father and mother -- and the fate of the whole city, in fact -- are also involved tragically in the prophecies surrounding Oedipus. For example, the father supposedly ordered the son left in the wilderness to die from exposure; this act of self-determination (or self-preservation), clearly taken to oppose the prophecy, didn't work and the father is killed by the son whom he had meant to have killed.
In this tragedy there doesn't seem to be much that one can do to oppose the pronouncements of fate.