How to find the inverse/reverse implementation of a function in theory?

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I have this concrete problem of reversing a function implementation: How to reverse this random number from a sequence generator function? But what I'm wondering for this question right here is, what is the general theory for finding the reverse implementation of a function? What are the techniques, how do you do it? Maybe if I knew that I could figure out this concrete problem on my own. But as of now, I am completely in the dark how I would find a solution to this problem.