bite off vs undertake

bite off

verb
  • To accept or commit oneself to a task, project, notion, or responsibility, especially one which presents challenges. 

  • To bite so hard as to remove something from its source. 

  • To acquire, especially in an abrupt or forceful manner. 

undertake

verb
  • To commit oneself (to an obligation, activity etc.). 

  • To pass a slower moving vehicle on the curbside rather than on the side closest to oncoming traffic. 

  • To take upon oneself; to start, to embark on (a specific task etc.). 

noun
  • The passing of slower traffic on the curbside rather than on the side closest to oncoming traffic. 

How often have the words bite off and undertake occurred in a corpus of books? (source: Google Ngram Viewer )