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The LDS mind does not comprehend a 'work of faith', even when it posts the example Paul gave of Abraham. So, just for readers of this thread, let's make an analogy:

When Abraham was taking Isaac to the place upon the mountain where he believed he was to make sacrifice to God, he told the servants to wait at the foot of the mount, that 'they' --he and Isaac-- would make the sacrifice and return to them at the foot of the mount. Abraham was making a work of faith in that he believed God' promises to him regarding making his descendants so numerous as to be like the sands of the sea. Abraham believed God would restore Isaac regardless, so that God would keep His promises. 'Abraham believed God and it was counted for him righteousness.'
Now the clue, as provided by Jesus speaking to Thomas after the Cross: Jesus saith unto him, "Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed."
When I place my faith in Jesus on my cross suffered He in my stead, then I act upon that belief by striving to keep the Two Great Commandments, God imputes to me righteousness, just as He did for Abraham in believing the promises of God. Thus salvation is by faith not of 'works' lest any man should boast. An act of faith is behaving as Jesus told the Pharisees was the work God required, as illustrated by Abraham's 'work of righteousness', where Abraham behaved according to his belief, his trust, in God's Promise.
A clue: Jesus told the Pharisees that David rejoiced 'to see His day'; Jesus taught them that 'blessed are they that have not seen, and yet have believed.'
Finally, Paul differentiates 'works of righteousness which we have done' and the work which God requires, which is trusting in His Promises, as illustrated with the example of Abraham and the trust Rahab exhibited and ultimately as Jesus illustrated perfectly in going willingly to the Cross trusting God would raise up the body and 'not allow His Holy One to see corruption'. Trusting in God's Promise is a different 'work' than something one does in pride of self, such as charity work trying to earn God's favor.