I am not sure about the "3,000 watts". That seems very low for your RW.
Inverters are fine however the type of connected loads is a consideration. I had Onan install a 6.5 KW (6,500 watts) generator to handle our two heat pumps, washer and dryer, dishwasher and fireplace. Generators should only carry 80% of their maximum load for best service. Induction loads, such as motors require a higher starting current than when running. A limited number of today's RV's have energy management computers coordinating the various power demands which could allow one to slightly down size the power source. For the rest of us a power source capable of handling random starting loads determines the sizing of the gen or power source.
Bob and Carol - Lees Summit, MO,
2016 Silverado 3500 HD, High Country DRW diesel, 3.73 gear ratio, long bed, 25K Reese Elite removable hitch with 2013 Redwood 36RL with 17.5" H-rated tires and MOR/ryde heavy duty shackle links and bushings; 6.5 KW gen