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So I have no idea if this has a name but my goal was to make a formula for kind of "bending" a fuction, say f, by another, g. I managed to figure out the parametric equations for it but can't solve them (which is my question, how could I solve them). (I did confirm that they work using desmos though.) Here are the equations:

$x=t-sin(arctan(g'(t)))f(t)$

$y=g(t)+cos(arctan(g'(t)))f(t)$

Thanks!

edit: Basically what I'm trying to do here is kind of like adding the functions but also rotate the other one to match the slope of the other at each point.

editx2: Here's my testing of the equations to give a clearer picture: https://www.desmos.com/calculator/kvhetjfgxt

editx3: I really typed those equations out wrong sry about that, also didn't know desmos can just fill in t:s so changed the link

wijo
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    What’s your question? – bubba Apr 15 '22 at 11:41
  • Welcome to math.SE! <> Is this the sort of thing you have in mind? https://math.stackexchange.com/questions/1238534/is-imposing-one-function-onto-another-ever-used-in-mathematics – Andrew D. Hwang Apr 15 '22 at 11:52
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    I doubt that this construction has a name, so you can make one up. Your description in words is not at all clear, If you really need a general construction and not just this particular example then at the least you should provide more examples - preferably ones with much simpler functions $f$ and $g$. – Ethan Bolker Apr 15 '22 at 14:31
  • I mean in the desmos link you can try any examples you'd like, I feel that's a lot better than trying to verbally describe stuff, but ty for feedback! – wijo Apr 15 '22 at 14:35

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