Are two functions equal?

Question

[Edit]

The general question seems incredibly hard to solve. Here is a significantly restricted version of this question.

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How do I dete

Answer 1

This is impossible according to Rice's theorem:

In computability theory, Rice's theorem states that, for any non-trivial property of partial functions, there is no general and effective method to decide whether an algorithm computes a partial function with that property.

If you restrict the domain of the functions to be finite, then you can trivially verify if ∀x: f(x) = g(x) using brute force, but this is not possible with an infinite domain.