Final answer:
The cell membrane maintains homeostasis through osmosis by being selectively permeable, thus controlling the balance of solutes and water across the cell, and preventing lysis or shrinking of the cell.
Step-by-step explanation:
The cell membrane is crucial for maintaining homeostasis within the cell through the process of osmosis. First, the cell membrane's selectively permeable nature prevents equilibrium between the intracellular and extracellular environments; it allows some molecules to pass while blocking others. Secondly, in the face of varying environmental conditions such as temperature and diet, the cell uses osmosis to balance the concentration of solutes inside and outside of the cell. Lastly, the regulation of water movement through the cell membrane by osmosis ensures that cells do not lyse or shrink, thereby maintaining a stable internal cell environment regardless of external conditions.
In conclusion, the semipermeable nature of the cell membrane is essential for osmotic balance and the maintenance of homeostasis within the cell. Without this critical function, cells would not be able to sustain the necessary conditions for life.