It's like いく. Maybe ゆくis a bit less conversational, but it's used a lot. So, 出かけてゆく would mean something like "go out and go (somewhere), instead of 出かけています "I'm out (right now)". Putting an いく after a te-form verb means that you'll do the verb first, then go. You can do the same with 来る, 帰る etc. 買ってくる: I'll buy it and come back. Or something a bit more famous(?): 行って来ます: (maybe it's in hiragana usually, but to clarify) I'll go and come back, but used in a sense like "see you later".

te yuku means based on iku as to go. sometimes you use it as something it won't come back. satteyuku 去ってゆく　 to leave ( leave and go, disappear) chitteyuku 散ってゆく　blossom/ leaf to fall.

I've heard it's an old/archaic thing, used by poets now similar to English writers may use "ye" or "thy"... Regards