The booster of course is a signal booster for the television. That 12v plug can be used for most any appliance. I assume the inverter you refer to is to provide 120v AC power. An inverter has a huge amperage requirement. Plugged into a running auto is one thing but it will drain your RV battery in a hurry. Check the amperage requirement on the inverter and check the fuse rating on this circuit.
Paul & Sheri - Upstate New York - SUN-0258
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2012 F150 F/X 4, 6cyl EcoBoost, Max Tow pkg
2013 Rockwood 8280WS 5th wheel
2006 Sunline Solaris T-1950