Identify the subject and verb in the sentence "with a smile on his face, Dad invited me to eat with him"

the subject is Dad and the verb is invited

The subject in a sentence is the person, animal or object that performs the main or direct action. The action is the verb of the sentence. In this case, Dad is the subject of the sentence because he is the one who is performing the main action or verb. In the sentence the verb is invited, because it is the action that Dad is performing.