" In short there is absolutely NO reason to not be backing up. Time Machine is a feature within OS X and all that is needed is an external HD."
it would have been nice to actually get some useful advice rather than telling off!
i've been using macs since the classic and have always managed to retrieve my files one way or another... in fact I managed to retrieve all my important stuff; I installed Yosemite on an external HD I had and managed to boot from it and collect my files that way... I tried repairing the disk from utilities but got a window saying "Disk Utility can't repair this disk. Back up as many files as possible and reformat the disk." ... I shut the computer down, unplugged the HD and restarted... the screen went straight to the Command R one... I opened up Utilities and attempted to erase the disk so I could reformat it... I then got this window "Disk Erase failed with the error. The given file system is not supported on Core Storage".... I restarted and tried again only to notice that my image file no longer appears, just the main HD (see attached pic) but it does show available space as 3TB so I guess it did erase of sorts; 
I then plugged in the HD I loaded Yosemite on and restarted to see if the image appeared with Disk Utilities that way... no luck; I obviously can't reinstall a new OS as the install procedure can't find the iMac OS.
On the one hand I've managed to get the files (which was crucial) but I seemed to have made matter worse... how can I get the image file to appear again?
Here's the blurb I got when I ran a repair on "Macintosh HD" above (I'm trying to get the photos I took from the Errors and progress report from the iMac Disk as I think it has some important info)Utilitie:
Verifying and repairing partition map for “APPLE SSD SM128E Media”Checking prerequisitesChecking the partition listAdjusting partition map to fit whole disk as requiredChecking for an EFI system partitionChecking the EFI system partition’s sizeChecking the EFI system partition’s file systemChecking all HFS data partition loader spacesChecking booter partitionsChecking booter partition disk0s3Repairing file system.Checking Journaled HFS Plus volume.Checking extents overflow file.Checking catalog file.Checking multi-linked files.Checking catalog hierarchy.Checking extended attributes file.Checking volume bitmap.Checking volume information.Trimming unused blocks.The volume Boot OS X appears to be OK.File system check exit code is 0.Updating boot support partitions for the volume as required.Reviewing boot support loadersChecking Core Storage Physical Volume partitionsVerifying storage systemChecking volumedisk1s2: Scan for Volume Headersdisk0s2: Scan for Volume Headersdisk1s2: Scan for Disk Labelsdisk0s2: Scan for Disk LabelsLogical Volume Group 15F8E573-67DB-4940-B78D-F73391D8DCC1 spans 2 devicesdisk0s2+disk1s2: Scan for Metadata VolumeLogical Volume Group has a 4481 MB Metadata Volume with double redundancyStart scanning metadata for a valid checkpointLoad and verify Segment HeadersLoad and verify Checkpoint PayloadLoad and verify Transaction SegmentIncorporate 0 newer non-checkpoint transactionsLoad and verify Virtual Address TableLoad and verify Segment Usage TableLoad and verify Metadata SuperblockLoad and verify Logical Volumes B-TreesLogical Volume Group contains 0 Logical VolumesLoad and verify Freespace SummaryLoad and verify Block AccountingLoad and verify Live Virtual AddressesNewest transaction commit checkpoint is validLoad and verify Segment CleaningThe volume 15F8E573-67DB-4940-B78D-F73391D8DCC1 appears to be OKStorage system check exit code is 0.Repairing storage systemChecking volumedisk1s2: Scan for Volume Headersdisk0s2: Scan for Volume Headersdisk1s2: Scan for Disk Labelsdisk0s2: Scan for Disk LabelsLogical Volume Group 15F8E573-67DB-4940-B78D-F73391D8DCC1 spans 2 devicesdisk0s2+disk1s2: Scan for Metadata VolumeLogical Volume Group has a 4481 MB Metadata Volume with double redundancyStart scanning metadata for a valid checkpointLoad and verify Segment HeadersLoad and verify Checkpoint PayloadLoad and verify Transaction SegmentIncorporate 0 newer non-checkpoint transactionsLoad and verify Virtual Address TableLoad and verify Segment Usage TableLoad and verify Metadata SuperblockLoad and verify Logical Volumes B-TreesLogical Volume Group contains 0 Logical VolumesLoad and verify Freespace SummaryLoad and verify Block AccountingLoad and verify Live Virtual AddressesNewest transaction commit checkpoint is validLoad and verify Segment CleaningThe volume 15F8E573-67DB-4940-B78D-F73391D8DCC1 appears to be OKStorage system check exit code is 0.Updating Windows boot.ini files as requiredThe partition map appears to be OK
Verifying partition map for “APPLE SSD SM128E Media”Checking prerequisitesChecking the partition listChecking for an EFI system partitionChecking the EFI system partition’s sizeChecking the EFI system partition’s file systemChecking all HFS data partition loader spacesChecking booter partitionsChecking booter partition disk0s3Verifying file system.Checking Journaled HFS Plus volume.Checking extents overflow file.Checking catalog file.Checking multi-linked files.Checking catalog hierarchy.Checking extended attributes file.Checking volume bitmap.Checking volume information.The volume Boot OS X appears to be OK.File system check exit code is 0.Checking Core Storage Physical Volume partitionsVerifying storage systemChecking volumedisk1s2: Scan for Volume Headersdisk0s2: Scan for Volume Headersdisk1s2: Scan for Disk Labelsdisk0s2: Scan for Disk LabelsLogical Volume Group 15F8E573-67DB-4940-B78D-F73391D8DCC1 spans 2 devicesdisk0s2+disk1s2: Scan for Metadata VolumeLogical Volume Group has a 4481 MB Metadata Volume with double redundancyStart scanning metadata for a valid checkpointLoad and verify Segment HeadersLoad and verify Checkpoint PayloadLoad and verify Transaction SegmentIncorporate 0 newer non-checkpoint transactionsLoad and verify Virtual Address TableLoad and verify Segment Usage TableLoad and verify Metadata SuperblockLoad and verify Logical Volumes B-TreesLogical Volume Group contains 0 Logical VolumesLoad and verify Freespace SummaryLoad and verify Block AccountingLoad and verify Live Virtual AddressesNewest transaction commit checkpoint is validLoad and verify Segment CleaningThe volume 15F8E573-67DB-4940-B78D-F73391D8DCC1 appears to be OKStorage system check exit code is 0.The partition map appears to be OK
Verifying and repairing partition map for “APPLE HDD ST3000DM001 Media”Checking prerequisitesChecking the partition listAdjusting partition map to fit whole disk as requiredChecking for an EFI system partitionChecking the EFI system partition’s sizeChecking the EFI system partition’s file systemChecking all HFS data partition loader spacesChecking booter partitionsChecking booter partition disk1s3Repairing file system.Checking Journaled HFS Plus volume.Checking extents overflow file.Checking catalog file.Checking multi-linked files.Checking catalog hierarchy.Checking extended attributes file.Checking volume bitmap.Checking volume information.The volume Recovery HD appears to be OK.File system check exit code is 0.Updating boot support partitions for the volume as required.Reviewing boot support loadersChecking Core Storage Physical Volume partitionsVerifying storage systemChecking volumedisk1s2: Scan for Volume Headersdisk0s2: Scan for Volume Headersdisk1s2: Scan for Disk Labelsdisk0s2: Scan for Disk LabelsLogical Volume Group 15F8E573-67DB-4940-B78D-F73391D8DCC1 spans 2 devicesdisk0s2+disk1s2: Scan for Metadata VolumeLogical Volume Group has a 4481 MB Metadata Volume with double redundancyStart scanning metadata for a valid checkpointLoad and verify Segment HeadersLoad and verify Checkpoint PayloadLoad and verify Transaction SegmentIncorporate 0 newer non-checkpoint transactionsLoad and verify Virtual Address TableLoad and verify Segment Usage TableLoad and verify Metadata SuperblockLoad and verify Logical Volumes B-TreesLogical Volume Group contains 0 Logical VolumesLoad and verify Freespace SummaryLoad and verify Block AccountingLoad and verify Live Virtual AddressesNewest transaction commit checkpoint is validLoad and verify Segment CleaningThe volume 15F8E573-67DB-4940-B78D-F73391D8DCC1 appears to be OKStorage system check exit code is 0.Repairing storage systemChecking volumedisk1s2: Scan for Volume Headersdisk0s2: Scan for Volume Headersdisk1s2: Scan for Disk Labelsdisk0s2: Scan for Disk LabelsLogical Volume Group 15F8E573-67DB-4940-B78D-F73391D8DCC1 spans 2 devicesdisk0s2+disk1s2: Scan for Metadata VolumeLogical Volume Group has a 4481 MB Metadata Volume with double redundancyStart scanning metadata for a valid checkpointLoad and verify Segment HeadersLoad and verify Checkpoint PayloadLoad and verify Transaction SegmentIncorporate 0 newer non-checkpoint transactionsLoad and verify Virtual Address TableLoad and verify Segment Usage TableLoad and verify Metadata SuperblockLoad and verify Logical Volumes B-TreesLogical Volume Group contains 0 Logical VolumesLoad and verify Freespace SummaryLoad and verify Block AccountingLoad and verify Live Virtual AddressesNewest transaction commit checkpoint is validLoad and verify Segment CleaningThe volume 15F8E573-67DB-4940-B78D-F73391D8DCC1 appears to be OKStorage system check exit code is 0.Updating Windows boot.ini files as requiredThe partition map appears to be OK
Verifying partition map for “APPLE HDD ST3000DM001 Media”Checking prerequisitesChecking the partition listChecking for an EFI system partitionChecking the EFI system partition’s sizeChecking the EFI system partition’s file systemChecking all HFS data partition loader spacesChecking booter partitionsChecking booter partition disk1s3Verifying file system.Checking Journaled HFS Plus volume.Checking extents overflow file.Checking catalog file.Checking multi-linked files.Checking catalog hierarchy.Checking extended attributes file.Checking volume bitmap.Checking volume information.The volume Recovery HD appears to be OK.File system check exit code is 0.Checking Core Storage Physical Volume partitionsVerifying storage systemChecking volumedisk1s2: Scan for Volume Headersdisk0s2: Scan for Volume Headersdisk1s2: Scan for Disk Labelsdisk0s2: Scan for Disk LabelsLogical Volume Group 15F8E573-67DB-4940-B78D-F73391D8DCC1 spans 2 devicesdisk0s2+disk1s2: Scan for Metadata VolumeLogical Volume Group has a 4481 MB Metadata Volume with double redundancyStart scanning metadata for a valid checkpointLoad and verify Segment HeadersLoad and verify Checkpoint PayloadLoad and verify Transaction SegmentIncorporate 0 newer non-checkpoint transactionsLoad and verify Virtual Address TableLoad and verify Segment Usage TableLoad and verify Metadata SuperblockLoad and verify Logical Volumes B-TreesLogical Volume Group contains 0 Logical VolumesLoad and verify Freespace SummaryLoad and verify Block AccountingLoad and verify Live Virtual AddressesNewest transaction commit checkpoint is validLoad and verify Segment CleaningThe volume 15F8E573-67DB-4940-B78D-F73391D8DCC1 appears to be OKStorage system check exit code is 0.The partition map appears to be OK
