Wiktionary
alt. (context transitive US English) to ask about the health of someone. vb. (context transitive US English) to ask about the health of someone.
Usage examples of "inquire after".
But she seemed to be so much out of the way, and to have no room to inquire after me, that I thought I was safe enough.
I wish you a good morning, and will pay my devoirs in a day or two to inquire after your health, and hear what has taken place.
The next morning, about nine o'clock, he sent to inquire after the health of his protegee and was answered by a request that he would pay her a visit.
She also noticed that no one made any effort to help the fallen men up, or to inquire after their well-being.
But because Thou dost not narrowly inquire after sins, we hope with confidence to find some place of indulgence with Thee.