Your backup may work properly, but this is not guaranteed.
Akeeba Backup / Akeeba Solo detected that your PHP configuration dissallows the use of certain functions. This is a normal security precaution taken on commercial hosts, but it might interfere with your backup process. The usual set of disabled functions for security reasons doesn't affect the operation of Akeeba Backup / Akeeba Solo. However, some hosts are very eager to disable lots of functions, some of them with low or inexistent security implications. If some of those functions are used by Akeeba Backup / Akeeba Solo, then your backup will fail with a PHP error, an empty AJAX error or a blank page.