Farrah Abraham -- BUSTED Over Sex Tape!

Farrah Abraham is as fake as her boobs ... having the nerve to claim she never signed on for a porn sequel. She did, and we have the email to prove it.

Abraham is upset over Vivid releasing a follow-up video to "Backdoor Teen Mom" ... claiming she never approved a sequel.

Small problem ... We have an email Farrah sent to Vivid ... in which she gives the porn company the right "to release video or Videos(s)." Plural times 2.

Farrah says she's a public figure, not a porn star. Fact is she's both -- she's a porn star who has a public figure, from both the front and the rear.