With the kind of family that I have, I do not think I could feel betrayed in any way. I have a family that loves me and that I love as well. It's a family that has always taken care of me and has never failed to do so.
However, finding out that I do not originally belong to this family may make me question and wonder who my original parents were, what they did, how they lived, how I am like them, and if they are still alive, if there are any fortunes that they left for me, or anything at all.
If they are still alive and perfectly fine, I may try to reach out to them just to connect with them. If they turn out to have genuine reasons for not finding me, I'd try to establish and keep that connection with them, but I will still belong to my current family. If my original parents did not have genuine reasons for leaving me, I would leave them alone and move on with my life.
This kind of scenario will surely bring up many questions in our minds. We will be curious if their life is better than us or worst than us. The true blood that runs in our veins will surely take the domination of our feelings.
In every situation there's always a reason behind it whether it's good or not that good, we must always remember to move forward and not be stock in the past. Whatever it may be.