Don't mistake F. Alexander for an ineffectual bookworm. He's a political dissident, and one so committed to his anti-Government vision that he's willing to sacrifice any number of individuals for it, including Alex…or especially Alex.
But let's backtrack a bit. The first time we meet F. Alexander is in the second chapter of the book, when Alex and his buddies break in to F. Alexander's house, tear up the writer's manuscript (which is entitled A Clockwork Orange, btw) and rape his wife. The wife later dies, and F. Alexander turns his grief into rage against the Government. A revolutionary is born.
Then, after Alex has been subjected to the Ludovico technique, he seeks shelter at F. Alexander's. F. Alexander recognizes him from the newspapers and takes pity on him—to him, Alex is just another victim of the Government:
"The tradition of liberty means all. The common people will let it go, oh yes. They will sell liberty for a quieter life. That is why they must be prodded, prodded— Eat well, poor boy, poor victim of the modern world." (3.5.12)
F. Alexander's plan is to use Alex (who has been beaten within an inch of his life because he can't fight back) as evidence that the Ludovico technique is monstrous and that the government is corrupt. He is, of course, correct. But, thanks to Alex's distinctive speech pattern, F. Alexander slowly realizes that Alex is the man responsible for his wife's rape and eventual death.
His thirst for revenge gets the better of him, and he locks Alex up in a room and blasts classical music (knowing that the Ludovico technique has made listening to classical music unbearable for Alex) until Alex jumps out the window, breaking several bones. The last we hear about F. Alexander is that he's been locked up:
"He had this idea," said the Min. "He was a menace. We put him away for his own protection. And also," he said, "for yours." (3.6.69)
The character of F. Alexander—like many of the characters in A Clockwork Orange—leaves us with more questions than answers. Was his rebellion against the Government always just a form of revenge-seeking? Did he want Alex to kill himself? And what about that name—since both he and the protagonist are named "Alexander," it seems that the reader is being asked to find similarities between the two. What might these similarities be?