If you define “work” as anything that a person does, then faith, too, perforce becomes a work. The thing is, it’s not a meritorious work (any more than reaching out your hands to receive a gift means that you somehow merit that gift — nonsense).

The Lutheran Confessions define “work” in a way I’ve found useful: It defines a “work” as something we offer to God.

Thus faith, by which we receive God’s gift, is not a work, even though we are active in it, because we only receive and do not offer in the exercise of that faith. (I’m talking about justifying faith.)

Thus, also, baptism and the Supper are not works, because we receive God’s gifts in those rites rather than offer gifts to him.

Good works are of course works, because by them we offer to God. They are just not justifying works.