OS X Using FileVault with OS X Recovery
FileVault and Legacy FileVault are both compatible with the Recovery System included with OS X Lion and later.
Starting up from OS X Recovery
To start from OS X Recovery with FileVault enabled, start up your Mac with the Command and R keys held down on the keyboard. Once you see the Apple logo appear you can release these keys. The Recovery System opens normally and you can perform any of the tasks that are listed.
To mount, verify, or repair a drive or volume that is encrypted with FileVault using Disk Utility, enter the FileVault password when prompted.
Some startup key combinations, such as those which use the Option or Command keys, may not be recognized if a firmware password has also been enabled. Firmware (EFI) passwords are different than FileVault passwords.
If you have a firmware password enabled on your Mac, you must successfully enter that password before you can start from another volume, or before you can access the Startup Manager.