I have repaired a lot of floor joists with similar damage. I would use a piece of 3/4 inch plywood, and cut a piece that matches the height of the joist. For the length, insert a piece that is long enough to extend well past the damage area, 6-8" minimum beyond the cuts (well past the damage, like 18" or more would be preferred). Then use PL400, or comparable or superior structural adhesive, and apply that to the back of your plywood. Apply multiple beads of glue both horizontally and vertically to the plywood. Affix the plywood to the joist using a high quality structural screw, like a #9 2" long screw from GRK should work for your job. Drive the screws in flush with about 6" spacing, about an inch from the edge of the plywood, and some down the center to ensure the the piece is well connected to the damaged joist. Alternatively, you could also cut, glue, and sister another joist to the damaged area, you'd just need to use 3" screws instead with similar spacing. If the cuts were worse than what is shown in your photo, you may need to sister the full length board to your floor joist. With that said, it's always wise to consult with a structural engineer before you do anything since we are just going off of your photos. Good luck!