Well, if you are not even seeing the partition, then F11 will not work - even if you could "fix" F11, there would still not be a recovery partition to use.  If you don't have some unknown partition on your disk, then you cannot use the factory restore and there is no way to restore that partition.
Hi! Some months ago, I recovered my O.S (Windows 7 X64) from the CD provided by DELL in buy moment. I'm trying to restore from the recovery partition, but there are not any! I only have one partition and it's the system partition, No Diagnostics and No Recovery.  Exits a place where I can download an HDD image of my DELL Studio 1747? Thanks a lot.
Recovery Partition