It's like jbrains762 said, either besvara or svara på. With svara + question, the preposition is compulsory. (You say Jag svarar henne 'I answer her', so the recipient of the answer does not need a preposition, only the question).
It seems to me that 'answer on such a question' has a slightly different meaning in English.
Do you mean a preposition? As in there's no replacement for på in English? If that's your question, English just doesn't use one. English does have a preposition in the phrase answers to, but that has the meaning of responsibility and having to answer any question, which is almost the opposite meaning to the sentence. Swedish svara requires a preposition, though you could besvara instead which does not.