Do power inverters run on energy from fossil fuels?

Usually a power inverter runs from a battery and generates alternating current from the direct current battery source.

So the question really is: Where does the battery get its energy?
If it is from a car battery then it is probably using gas or diesel fuel, fossil fuel
If it is connected to a battery bank running on solar cells or a windmill or a water wheel, then it is not using fossil fuel.
So my answer is: Maybe.

I'm doing this for a project on solar energy to power a home, so I think I'm good :).

Good, yes.

Also, are there any other backup systems for solar power other than just batteries?

Power inverters do not directly run on energy from fossil fuels. A power inverter is a device that converts direct current (DC) electricity into alternating current (AC) electricity. The DC electricity can come from various sources, such as batteries, solar panels, or even a car's electrical system.

That being said, the energy source used to charge the batteries or power the devices connected to the inverter can come from various sources, including fossil fuels. For example, if you connect a power inverter to a battery that has been charged using electricity from a coal-fired power plant, then indirectly, the power inverter would be utilizing energy from fossil fuels.

However, power inverters themselves are not dependent on fossil fuels. They are simply a means of converting the type of electricity being used, and the energy source depends on what is connected to the inverter.