Even though "think" is generally translated to "penser", I think here, it is better to use "réfléchir", which is more deep. - Avez-vous déjà réfléchi à cette question, Also for "the purpose of life" there is an expression which is - quel est le sens de la vie ? So sense is used instead of purpose, if you want to use purpose I think the suggestion by Marlon is great, "existence" fits better here than "vie", as in Aysel suggestion. - quel est le but de l'existence ? ( REM: It is not to be mistaken with "what is your goal in life ?", which has a different meaning - quel est votre but dans la vie ? ) Another expression is common, but it sounds slightly pessimistic or nihilist. - à quoi ça sert de vivre ?

Simple: Avez-vous jamais pensé du but de l'existence? or Avez-vous jamais pensé de cette question: qu'est-ce qui est le but de l'existence?

Maybe it will be: "as-tu déjà pensé à cette question, quel est le but de la vie?" (maybe I have mistakes)