The meaning of impertinent are two:
- not showing proper respect; rude
- (formal) not pertinent to a particular matter; irrelevant
Hers was an impertinent question.
Talk of rhetoric and strategy is impertinent to this process.
At least in the second case, impertinent is an antonym of pertinent.
The original meaning of the word is the second one; the meaning then slowly changed to the first one.
The Wiktionary has a note about the usage of impertinent:
As many older speakers will consider definition 2 incorrect, avoiding the word altogether may be advisable. The construction "not pertinent" is one possible alternative.