The bathtub suddenly sagged an inch when someone was taking a shower. I went into the crawl space and discovered that the builder had cut out a portion of the floor joist that ran lengthwise under the middle of tub in order to plumb the tub.

A carpenter recommended jacking up the joist, then using a piece of floor joist to make a T at the end of the cut, nailing it into the cut joist and the two intact joists on either side of the cut joist, then remove the jack. Obviously, do this to both cut ends of the joist. Is that going to work? Will that pass a building inspector's inspection?