define function on two sets

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Your question is not very clear to me. I suppose that $X$ and $Y$ are finite sets. If you know a map from $X$ to $Y$ and you want to define it in SageMath, you may define a dictionary with keys $X$ and values $Y$ : define d = dict() and then d[x] = y for all pairs $(x,y)$ such that $y = f(x)$. If on the other hand you have $f$ defined in some way, such as a dictionary or something similar, and you want it truly as a function, you may write (I use the dictionary, known globally):

def f(x):
    if x in d:
        return d[x]
    raise ValueError("{} is not in the domain of f".format(x))

Could you please provide the sets and the function you want to deal with in Sage ?