Question

where do the proteins made by free ribosomes function? within the cytoplasm inside the nucleus other cells

Explanation:

Ribosomes are of two types: free ribosomes and bound ribosomes. Free ribosomes are located in the cytosol and synthesize proteins that function in the cytosol itself. Bound ribosomes are attached to the endoplasmic reticulum and synthesize proteins for secretion or for use in other organelles like the nucleus (but this is a more complex process involving transport). Proteins made by free ribosomes are not for other cells (that's more of a role for secreted proteins from bound ribosomes in some cases).

Answer:

within the cytoplasm