What is the main purpose of the cell membrane in living things

The function of a cell membrane is to protect the structures within the cell, give shape to the cell and support its structure.

you can't tell one function as main.

compartmentation,

viability

sorting of chemicals so that which molecule can pass and which cant

atp production complexes are buried inside that,

adhesion,

cell cell recognition by glycoproteins which are found on cell membrane. etc it does a lot of functions.

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what have fossils ever done for you

answer; a male inherits only one allele of the x-linked gene controlling hair color;