In US English, you should always use inquiry and inquiry, regardless of the formality of the investigation. In British English, inquiry and inquire are used to describe formal/official investigations and lines of questioning, whereas enquire and inquiry are used in less formal investigations.
These inquiries relate to a sentence's topic.
Yes or no/ Objective questions
The typical response to these queries is "yes" or "yes, of course" or "no" or "I'm sorry."
Prior to the subject, use the auxiliary verb: Do you still recall...? not ‘You do recall’.
Object questions
These inquiries concern the sentence's object:
Use an auxiliary verb (such as "do," "did," "had," "can," etc.) whenever possible: Which location would you prefer? not Where would you want to meet?
You may use this expression to ask a question in an email. It conveys your want to hear back.
Asking for updation
