Complex sentence: The "f" in the channel's name and logo was rendered in lower-case to portray a type of relaxed friendliness; the stylized "X" represented the channel's roots: the crossing searchlights of the 20th Century Fox logo.
Split into simpler sentences: The "f" was lower-case to portray a type of relaxed friendliness. The stylized "X" represented the channel's roots: the crossing searchlights of the 20th Century Fox logo.