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Define function using lists or tables

Hello. Possibly this is a very simple question.

Is there a way to define a function over a (BIG) list of ordered pairs? I mean, suppose that I have a list, created using a Table command or something like that, of the form [{a,b},{c,d},etc.] such that, after naming it f, say, f = [{a,b},{c,d},etc.], then, afterwards, whenever there is a command such that one needs to compute f[a] (or f[c]), the program immediately replaces f[a] by b,and f[c] by d?

Thank you.

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