I just want to ask if it is okay to say to your boss who is going home after work お疲れ様でした気をつけてください or it is impolite?
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Yes and no.
The phrase 気を付けてください alone is in polite form (towards a person of a higher standing slightly better would be: お気を付けてください). However it does feel a little bit more like "please take care" rather than casual English greeting "take care". It would be strange if you used the phrase every single time a person leaves.
To strangers or people with whom you rarely meet, or towards a person you meet every day, but in an unusual situation like a typhoon coming, a phrase お気を付けてお帰りください would be very appropriate.
Then again, you might contract it to the previous お気を付けてください, or お気を付けて depending on familiarity, context, characters left in an electronic message, etc. I guess your teacher considered your situation of being late to be unusual.
(お気を付けてください would be also appropriate for a variety of situations, like towards someone going for a business trip, going abroad for holidays, or when you want to be nice and show your gratitude for something (being invited to a dinner), but you asked specifically for "going home after work" and that might feel a bit strange repeated day by day)
(...yet again, if you make it a ritual to say so, you're good to go, then a shorter お気をつけて might work best, I guess)