Most businesses publish a more general mailbox such as sales@xxx.com or technical@xxx.com in their website or printed materials.

Always use Aliases for your general mailbox. Aliases receive email and automatically redirect to other email address that you specify. This is usually free and unlimited from your email hosting service provider. Check with them to find out the number of maximum email address you can specify (both outside domains and internals).
Imagine you have five sales representatives. Try to direct all emails from sales@xxx.com to every one of them at their individual mailboxes. Remember to add sales@xxx.com to the Bcc field when sending out emails from your sales representatives. On resignation (if any), what you have to do is to update the Aliases and make sure you forward it to the right person.