"I have not been able to answer your question."
Translation:Non ho potuto rispondere alla tua domanda.
why isn't there an "a" or "da" before "rispondere" here? How can I know whether an infinitive uses "a" or "da" or nothing at all?
Yes. Rispondere is an intransitive verb. Rispondere a is the most common form. You can also have rispondere di, to be responsible for, rispondere di no, to answer no, or rispondere che, to answer that.
Your could apply to more than one person, or to one person with the familiar or formal mode.