When Yosef reveals his identity to his brothers, his first question to them seems almost a non-sequitur. For a while now the entire conversation had revolved around Yaakov and his pain at losing Binyamin. Yehuda had just finished delivering an entire speech hinging on precisely that point. And then Yosef reveals his identity and asks if his father is alive.
Obviously Yosef was not asking a question to which he had already been told the answer many times. The difference now was not in Yakov's state of being in between Yosef's pretending to be an Egyptian and his revelation of his true identity, but in the identity itself. The change had not taken place in Yaakov, but in how the brothers now saw Yosef, and his question must be seen in that light.
To understand Yosef's question, Haod Avi Chai, Does My Father Still Live, we need to take a step back and look at the dynamic of Yaakov's family. Ever since the confrontation with Esav when Yaakov had chosen to appease his renegade brothers, and with the kidnapping of Dinah, a rift had existed between Yaakov and the sons of Leah.
Yaakov's elder sons were the children of an unfavored wife. And they were more aggressive than Yaakov was comfortable with being. And they had taken the lead and stopped listening to Yaakov during the abduction of Dinah, when they took the lead, spoke before their father to Chamor, and defended their actions to him. Reuven's actions in moving Yaakov's bed fall into that category.
Essentially Leah's older sons had taken over the leadership of the family, and when Yosef's dreams seemed to threatened that leadership, they disposed of him. By acting in this way, they had removed Yaakov's authority and behaved as if their father was already dead.
Now Yosef's first challenge to them on the revelation of his identity connects right back to the original power struggle that caused him to be enslaved. Is Yaakov alive and their father, or is the elder sons of Leah, who in turn are unable to answer him.
If we look back or forward to the Haggadah, which quotes the Midrash, Arami Oved Avi Vayered Mitzraima, an Aramean (meaning Lavan) tried to destroy my father and he descended to Egypt.
The obvious question is how did Lavan's actions force Yaakov to descend to Egypt? The gap in time alone seems to render null and void any connection. But what did Lavan do to try and destroy Yaakov? He tricked Yaakov by giving him Leah in place of Rachel, thereby creating a divided household and a breach in the family. This breach caused Yosef to be sent to Egypt and Yaakov to follow after him.
But Lavan's actions that would cause Yaakov to go down to Mitzrayim, were ultimately the will of G-d. Thus Lavan's plot to undermine Yaakov's family would instead only go on to fulfill G-d's plan for them. What Lavan thought would destroy Yaakov, instead kept the entire family alive as Yosef was able to provide for them.
And Yosef's question marks a basic power shift in the family, as Yosef now takes charge and leadership of Bnei Yaakov. It is he who provides for them, designates where they should live and at whose table they eat. It is his sons who are split into separate tribes, giving him a limited parity with Yaakov.
Yosef's question affirms his leadership, by asking them to affirm Yaakov's leadership. Haod Avi Chai. By recognizing that it is their father who rules, they are able to submit to Yosef. Yosef in turn recognizes the divine providence and instead of ruling over them, brings them inside.