Does anyone know how I can fix my Badger 100lg. When I was unscrewing the airhose from the airbrush, the part pictured in the photo just came off!!

If that's the air intake "valve" you may try some epoxy or solder? You'll just need something that won't leak air, you probably wont need something that can withstand high pressure since most ABing is done around 15-20 psi.

Time to bite the bullet and buy a new one, it seems to me. You may be able to get just the main body, as in the photo, but the cost (£30-£40) may not be worth while.

OK can finally see the image.
although it is a little dark, it appears the base for the air valve has become separtated from the main body. Unfortunately according to my parts diagram, this is not a replaceable/removeable part, and I can not see it it is threaded or soldered to the main body by the photo.
It is a soldered connection, and you have good soldering skills with small items, then solder it back together. If not, you can either retun the body to badger for repairs, or order a new body. the part number is:
50-0342
the parts diagram is here for future reference:
http://badgerairbrush.com/100lgparts.htm
and here is the info page on contacting them for repairs:
http://badgerairbrush.com/contact.htm
Although I have never had to send any of my Badgers in for repairs, others I know have, and say the service is excellent.

Rosen and some match solder. (low heat solder) same way you would sweat a copper pipe fitting