In today’s passage, we have the accounts of two healings, one of a person on the verge of death and the other of a person who had already died. Later in the chapter (vss. 36-50), Jesus forgives the sins of a notoriously sinful woman. Luke’s intent in chapter 7 is to show that Jesus is whom he claims to be—the Messiah, the Promised One sent by God. He’s able to heal the sick, raise the dead, and forgive sins, proving his claims to be the Messiah.
The two cases in view here are rather remarkable in that neither of the people who were healed expressed any faith in Jesus whatsoever. In the first case, the master of the servant had faith, but in the second case, no one other than Jesus had faith. God is sovereign and will heal or not heal according to his will and purpose, not based primarily on the faith of the one needing healing.