Find your tire / loading sticker (on drivers door or door post). It will show tire size, tire pressure, and max cargo / passenger weight (payload).
Cargo / passenger capacity gets used up by aftermarket accessories (bed liner, undercoating, bed cover, etc), people, pets, cargo, trailer tongue weight, and weight distributing hitch (about 100 lbs). Every pound you add to the vehicle, takes away a pound from both, towing capacity and available payload.
If you know how much capacity you have available for tongue weight, divide that number by .13. That will give you a loaded trailer weight that will put you in the ball park of your max weight capacity. A 9600 lb trailer, with a WD hitch, would eat over 1300 lbs of payload.
As mentioned above, the closer you get to max weight, the less pleasant your towing experience will be.
There are versions of the F150, with payloads everywhere between 750 lbs and 3200 lbs. The one with 3200 lbs payload, could tow that 9600 lb trailer.
According to RV dealers, an RV is half ton tow able as long as there is any half ton capable of towing it. They don't tell you, there may be many that either can't or shouldn't.