Question

If the environment outside a cell is hypertonic how will the cell maintain homeostasis

Answer 1

It'll maintain homeostasis by removing water molecules out from the cell to the outside.

This process is known as osmosis. Since osmosis is the movement of water molecules from a region of higher water potential to a region of lower water potential, through a partially permeable membrane, so as hypertonic means the outside has a lower water potential than the cell cytoplasm, so the cell loses water.

As the water molecules flow away form the cell, the cell might shrink, or plasmolysis may occur if in plant cells. Either way, net water movement will continue until both side of the water potential is the same, where equilibrium is achieved. At that time, water still moves, but the number of water molecules moving from the left to the right is the same to the molecules that moves from the right to the left.

Answer 2

Homeostasis, A cell membrane does not actually maintain homeostasis by itself. The term homeostasis refers to maintaining a relatively stable environment inside of a multi-cell organism. 

Hope this helped, If you need me to go more in detail let me know