SO fiddle

Test Fiddle mainly for SO Questions

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8/themes/dot-luv/jquery-ui.css">
<div id="page" style="background-image: url(xxx)">Click here to test the code</div>
<div id="page2">Click here for the negative test</div>

CSS

.clicked { color:red; }
#page.bg { color:green; }

JavaScript

$("#page, #page2").click(function () {
    $(this).addClass("clicked");
    $(this).addClass(function () {
        return $(this).css("background-image") ? "bg" : "";        
    });
});