What is the function and contribution to the novel of both Clarisse and Professor Faber in Fahrenheit 451?

Clarisse and Faber play similar roles in the book, in that they both introduce Montag to a new way of looking at the world.  Before meeting Clarisse, Montag never really questioned whether he was happy or not, and before meeting Faber, he never really thought about how things used to be. Meeting each of them helped move Montag along the road to subversion.

Clarisse is a teenage neighbor of Montag’s. When he meets her for the first time, she comments that she is not afraid of him, and she also asks him an unusual question.

She laughed at this. "Good night!" She started up her walk. Then she seemed to remember something and came back to look at him with wonder and curiosity. "Are you happy?" she said.

"Am I what?" he cried.

But she was gone—running in the moonlight. Her front door shut gently.

"Happy! Of all the nonsense." (Part I)

It had never occurred to Montag to wonder if he was happy or not, or even to think about being happy. Clarisse comments that he doesn’t seem to really listen when she talks, laughs when she is not being funny, and responds without thinking. Clarisse’s conversations really shake Montag. He starts to realize that not only is he not happy, he is supremely unhappy. He has tired of his shallow existence with Mildred and longs for more.

Montag steals a book, and finds that he doesn’t know what to do with it. Montag fears the repercussions of having the book, but he also doesn’t really know how to get into this alternative lifestyle that he knows exists. For this he looks up Professor Faber, whom he had previously met in a park.  When Clarisse questions him about being happy, he immediately thinks of Faber.

What a strange meeting on a strange night. He remembered nothing like it save one afternoon a year ago when he had met an old man in the park and they had talked.... (Part I)

While Faber is naturally skeptical about Montag’s desire to know more about books, and have someone to teach him, he convinces the professor that he is sincere. He wants more from life, and he doesn’t know how else to get it. He doesn’t believe Beatty when he says books are meaningless.

Both Clarisse and Faber serve as catalysts for Montag. Clarisse makes him question, and Faber makes him act on that questioning. He gains confidence in dealing with Beatty when Faber is walking him through things. When he goes on the run, he relies on the book people to guide him. Clarisse initially showed him the way, but Faber was his mentor.