As I understand it, faith is not belief in a proposition. In the bible faith is a work. That is right I said it is a work. Faith is the work of receptivity.
Christians are radically and dare I say foolishly gun shy of this word "works." Now if I come over to your house and do a ton of work and you pay me for the work I have done with a check for $3,000. Next I will put forth a little bit of effort and get myself down to the bank so I can cash that check. Did I earn that $3,000 by cashing the check? No I earned it by doing the work at your house. Is cashing the check something that requires some sort of effort on my part? Yes. Does my effort in cashing the check create the $3,000? No, the $3,000 already existed in your account. Can I go down to the bank and endorse any piece of paper and turn that into $3,000? No, I can only endorse checks made out by someone who actually has the money in their account. Cashing that check takes a bit of faith on my part that the bank will honor it and that the check is good.
What about the righteousness that comes by faith? Is that work too? Absolutely yes!
So too, Jesus worked to create for us this awesome gift of His life within us. However we do need to embrace the gift. Everything it cost Jesus to make that gift available is work we never did. We can embrace Jesus all day long 24/7/365 but if Jesus has nothing to give us then all our effort spent embracing Him will amount to little more than a hug. BUT if Jesus had a great gift to give us, with a little effort on our part to receive what He has provided freely then we will receive all that He is offering us.
Faith is the work of receptivity of Christ's activity. In this way righteousness is a work of faith. The indwelling Christ has made me an offer. He is willing to live in me, He will stay with me, He will encourage me and tell me that He adores me beyond description. As I put forth the work of abiding in Jesus, His character begins to grow inside me. I do not create it by myself, Jesus creates it for me and in me. However, I receive this gift of real actual righteousness whereby I become a loving, Christlike person down to the depths of my genuine true character and I obtain this reality by faith in the activity of my indwelling savior.