Page 9-23 of the 2015 Owner's Manual says the fuse is located in the passenger compartment fuse block, position 2 (Cigarette lighter) 15 amp.
Never install a fuse with a rating higher than specified for the circuit. The fuse not only protects the device using the electricity, but more importantly the wiring.
You are lucky that thing didn't incinerate your car. I'm glad you are okay.
For the record, what model inverter was it?
__________________________________________
View my fuel log 2015 Mirage ES 1.2 manual: 49.6 mpg (US) ... 21.1 km/L ... 4.7 L/100 km ... 59.5 mpg (Imp)