go at vs take up

go at

verb
  • To try to solve a problem a specific way; to undertake a task. 

  • Used other than figuratively or idiomatically: see go, at. 

  • To initiate an attack on or an argument with. 

take up

verb
  • To address (an issue). 

  • To accept (a proposal, offer, request, etc.) from. 

  • To implement, to employ, to put into use. 

  • To review the solutions to a test or other assessment with a class. 

  • To begin doing (an activity) on a regular basis. 

  • To occupy; to consume (space or time). 

  • Synonym of take in (“tighten a belaying rope”) 

  • To resume. 

  • To pick up. 

  • To shorten by hemming. 

How often have the words go at and take up occurred in a corpus of books? (source: Google Ngram Viewer )