Farnsworth "Dex" Dexter is the son of Blake Carrington's business partner Samuel Dexter, whose the member of the board of directors of "Denver-Carrington". He's a successful oilman and as a commando, who served in Vietnam during the war, he was involved in special military missions for the government.
In the beginning he's a self-centered associate of Blake's , who doesn't band so easily and doesn't break at all which means he doesn't respect other authorities. In the time, he becomes Blake's confidant and friend. On his arrival, Dex becomes lover and afterwards Alexis's husband, so they even decide to launch their private company named "Lex-Dex".
Their relationship will be full of passion but it'll go through many hard times when Alexis betrays him with Blake's business associate Rashid Ahmed. Finding them in Asian hotel suite together, furious and overmuch hurt Dex starts a very short affair with Blake's dismissed assistant Tracy Kendall and wants her to work for "ColbyCo. Oil" in order to keep an eye on Alexis. This sort of consent is, however, rather short-lived because Tracy decides to keep to her own line leaving Dex to hug himself over fruitless thought - whether they deny it or not, genuine feelings are always in sight.
Therefore, Alexis and Dex are back in the saddle, so to speak, and owing to him Alexis is no longer guilty of murdering Mark Jennings. Within a short time, Dex meets his old acquaintance Daniel Reece and, accompanied by him, reopens an ambiguous chapter of his life grappling with some new assignments but, on the occasion of Daniel's sudden death, he becomes entangled in Moldavian conspiracy and then in affair with Amanda so his marriage to Alexis is about to be terminated.
Everything gets much worse when Alexis starts scheming with Blake's brother Ben which leads to further disagreements, and even though Dex is still taking a fancy to her, Dominique stands for his new desire - such being the case, she and Dex meet his friend Sarah Curtis who's going to manage Krystina's heart surgery. For a long time Dex will put up with Alexis's wimps and her obsession with Blake, he'll even save her from psychotic Sean Rowan, all up to moment when Alexis finds out about the mysterious murder of Roger Grimes and starts going after the Carringtons.
Dex than starts a serious relationship with Sable, ex-wife of Jason Colby. He's caught in the middle of the conflict between Alexis and Sable. After one of the biggest scenes between Dex and Alexis in "The Carlton" hotel, they both fall down from the gallery as the fence of the balcony breaks before the horrified eyes of Adam, Sable and Monica. The fate of Dex is left a mystery because in the special sequel "The Reunion", it's not explained what happened with Dex after the fall.