Question

The domain that includes organisms with true nuclei and membrane-bound organelles is called *

Answer 1

Eukarya. Eukaryotes are the only organisms that have true nuclei and membrane-bound organelles, though some bacteria have a pseudo-nuclei.
The reason why only eukaryotes have true nuclei and membrane-bound organelles is because only eukaryotes have figured out how to create so much energy through the mitochondria, which is required for high compartmentalization.