actually, you have things mixed up.
nearly all RV's come with CONVERTERS, not INVERTERS.
converters do what you're asking about, charging batteries from shore power or from a generator. no different than a stand-alone battery charger.
an INVERTER changes battery DC power to AC power. it converts 12v power to 110v power for things like tv's, dvd players and other things you need to plug in.
inverters don't usually come standard on RV's, except on expensive Class A motorhomes. some MH's and 5th wheels offer them as an option.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC