In a single-celled organism, the absorption of oxygen and nutrients happens directly through the cell membrane.

Here's why:

* No Specialized Organs: Unlike multicellular organisms with complex organ systems, single-celled organisms lack specialized organs like lungs or intestines for absorption.

* Surface Area: Their entire surface area is in direct contact with the environment.

* Diffusion: Oxygen and nutrients move across the cell membrane by diffusion, a process where substances move from an area of high concentration to an area of low concentration.

So, in summary, the cell membrane is the key player in absorbing oxygen and nutrients for a single-celled organism.