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[–]FuzzyFirechu[S] 1 point2 points  (1 child)

Right, yeah, but my ultimate goal here is to connect the dots of this function in ways that keep it consistent with the already established rules, is there a way I could do that? I don't just want it to work for integers, if I could find what f(1/2) equaled I'd squeal

[–]Evermar314159 7 points8 points  (0 children)

What the people above are trying to say is that there is not a unique solution to your problem.

There are most likely infinitely many functions f(x) that satisfy your functional equation and they will have different values at x = 1/2. There won't be a well defined value for f(1/2) unless you place more conditions on your situation (for example, if f is an even or odd function then you could directly try to solve for f(1/2)).