How do I generate a function to satisfy given conditions.

I have a 6000 x 550 data matrix (X) and another 1 x 550 matrix (Y). I need to find a function such that the following holds true: mean(function(X))= Y . I do not know the form of the function and have no idea how to proceed. Is there any way to do this?
Cheers, Aditya.

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