Final answer:
The nucleolus, nuclear pores, and nuclear membrane are interconnected in the synthesis of ribosomal RNA and ribosome assembly, which is essential for protein synthesis.
Step-by-step explanation:
The functional connection between the nucleolus, nuclear pores, and the nuclear membrane is primarily related to the synthesis of ribosomal RNA (rRNA) and the assembly of ribosomes, which are vital components for protein synthesis. The nucleolus is responsible for producing and assembling rRNA and ribosomal subunits. Once these subunits are assembled in the nucleolus, they are then transported out to the cytoplasm through the nuclear pores in the nuclear envelope. Therefore, the correct answer is A) Synthesis of ribosomal RNA.