Undertake seriously to use bad language (5)
I believe the answer is:
swear
This clue could be a double definition.
'undertake seriously' is the first definition.
'swear' can be an answer for 'undertake' (thesaurus). I am not certain of the 'seriously' bit.
'use bad language' is the second definition.
(I've seen this before)
'to' acts as a link.
Can you help me to learn more?
(Other definitions for swear that I've seen before include "Affirm" , "Promise on oath" , "Emit oath or take vow" , "Vow, attest" , "Express annoyance" .)