I have a small 12 volt inverter that will handle 300 watts and plugs into a 12 volt port. It is not nearly big enough to handle a microwave or toaster or coffeemaker or hair dryer type appliances; it does well when we need to power 120 volt lamps, charge a computer, or watch a small TV.
My 300 watt inverter is at best 80% efficient at full load, so it is drawing close to 360 watts from the battery. That means it is drawing about 30 amps.
A pair of car head lights draws about 120 watts. So in rough figures, how long would your battery last if you had to power three automobile with their headlight on and their motors off? And, that is only asking for 300 watts.
The bottom line is it can be done but you have to understand your energy needs. They can accumulate quite rapidly.
There is a reason most folks just opt for a generator.