In all propability this infection is not restricted to functions.php only. Non WordPress files on your server might be infected as well as well as your wp-config.php and your db. Hackers do quite a good job when they hack a site.
Simply deleting (which will in all propability break your site leaving you with WSOD) and replacing functions.php will most propably never fix your issue, and if it even solve the issue, it will definitely not be long before you encounter the same issue, so the whole exercise will be useless.
You need to work through your theme and close the loop holes, this is VERY VERY IMPORTANT. Also, hire a professional, it will be worth it, to totally get rid of the infection and to work throught your theme and give you advice on possible loop hole.
Also make sure you are up to date with PHP and WordPress versions