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Reflection Over a Graph

On Reddit u/__math_nerd wondered about reflecting a function over another function. I asked for more, and made this to poke around with the idea. Conversation was: u/__math_nerd: Has anybody discovered how to reflect a non linear function, over another non linear function yet? If not, then I may be the first to have discovered how. I just ask, if anybody knows if it's been done, and proven before, can you show me? I looked everywhere and cant seem to find a work similar to mine, so I think mine may be perfectly original. TL:DR Basically I may have discovered how to reflect a non linear function, over another, and I want to know if I did discover it, or if it's been done before. >Pointwise? That would just be a difference, right? f(x)-(g(x)-f(x)). Maybe an image of what you mean? No, let's simplify. Imagine reflecting y=x2 over y=x You get a set of points of the reflected function >over a line it makes sense, but what do you get reflecting y=x over y=x2? If you mean a geometric reflection, it would be like for each point in the graph reflecting over where the perpendicular hits the graph of reflection? I love the big thinking, but don't know what you mean yet. You explained perfectly what I said. So just follow what you typed, and that's what it means, sorry I'm such a terrible explainer