To the op If your unit has a residential refrigerator, an inverter will be running it.
If your frige is gas/elec then it doesnt need an inverter and the most likely unit would be a small one powering a television and entertainment setup unless the prior owner installed another one.
Easiest way to test would be to unplug from shore power and then try each outlet to see if it is getting AC power. You can test by plugging in a droplight or whatever.
Most common places to find that someone has added one would be kitchen counter,dinette areas (as you mentioned for coffee and computer use) and the bedroom area for CPAP use.