How do you normally respond if you do not know a customer's request?

That depends on the scenario. If the person asks something which is out of your domain then, by all means, say you do not have the answer. However, you will get back to him/her with the right answer and or with the appropriate people who can provide him appropriate details of his/her inquiry. NEVER ever assume and always always ask for help if need be. If you noticed I put a stressed on NEVER and always because that is exactly what you need to remember always. 

Give assurance to the customer that you will assist her and provide an update if need be and you will just be fine. This is what you also call ownership and accountability. Anyway, should you need to refer the customer to another department who can best answer his/her inquiry, as FPOC you have done a great job.