The organelle with membrane-bound structures inside a cell that perform specialized functions is the endoplasmic reticulum (ER).

Here's why:

* Membrane-bound: The ER is a network of interconnected membranes that extend throughout the cytoplasm of eukaryotic cells.

* Specialized functions: The ER has two main forms:

* Rough ER: studded with ribosomes, which are responsible for protein synthesis and folding.

* Smooth ER: lacks ribosomes and is involved in lipid synthesis, detoxification, and calcium storage.

While other organelles like mitochondria, Golgi apparatus, and lysosomes also have membrane-bound structures, their functions are distinct from the ER's role in protein synthesis, lipid metabolism, and other cellular processes.