Now I know this basic question has been asked before, but I must be doing something wrong. I know that an appended element must bound before I can do anything to it. However
If I understand your question correctly, I've made a fiddle that has this working correctly. This issue is with how you're assigning the event handlers and as others have said you have over riding event handlers. The current jQuery best practice is to use on() to register event handlers. Here's a link to the jQuery docs about on: link
Your original solution was pretty close but the way you added the event handlers is a bit confusing. It's considered best practice to not add events to HTML elements. I recommend reading up on Unobstrusive JavaScript.
Here's the JavaScript code. I added a counter variable so you can see that it is working correctly.
$('#answer').on('click', function() {
feedback('hey there');
});
var counter = 0;
function feedback(message) {
$('#feedback').remove();
$('.answers').append('' + message + ' ' + counter + '');
counter++;
}