Hi renaldo,
A 4kW inverter will draw something like 400A from your 12V battery. A big starter battery for a diesel pickup can supply 400A for a few seconds but the voltage at this current will drop to about 10.5V this will raise the current to 460A. I recommend using a higher voltage like 24 or 48 Volts, this way the current will be half or one fourth compared to 12Volts input. Even at these higher voltages you need big powerful truck batterys. The commercial inverters for 12 V input are seldom above 1000 W continuous power, and for a good reason!