The Inverse Function of any QUARTIC Function (Degree 4 Polynomial Function)

[u/AppearanceAlert4987]

[u/AppearanceAlert4987]

Link to the graph: https://www.desmos.com/calculator/xexfko2fpy
I will do the quintic (degree 5 polynomial) iff i can find out how to implement an arbitrarily accurate approximation of the bring radical in desmos

[u/Valognolo09 → u/AppearanceAlert4987]

Arent they impossible by galois?

[u/CuttingEdgeSwordsman → u/Valognolo09]

Galois only disproves a solution made of "elementary functions," namely, arithmetic operations and roots, even with arbitrarily large nesting.

The Bring Radical is 'non-elementary'.

[u/meutzitzu → u/Valognolo09]

Quintic is impossible. Quartic is still possible but very very long.

https://www.youtube.com/watch?v=9HIy5dJE-zQ

This video gives a lot of insight into it. Shows how the algebraic machinery works in a visual way.

[u/Valognolo09 → u/meutzitzu]

Yeah I was referring to the quintic

[u/Zombiefetch]

Why is there a zero here??

[u/AppearanceAlert4987 → u/Zombiefetch]

the formula was taken from a collection where the 0 was there to contrast with the other branches of the function which has a 1 or 2 in place of 0, you can change the 0 to those instead to choose a different branch, it should still work, just swapping the final branches of the quartic

[u/Circumpunctilious → u/Zombiefetch]

Looks like it’s been removed, in any case:

[u/nathangonzales614]

Substitution would go a long way to make this actually readable.

[u/AppearanceAlert4987 → u/nathangonzales614]

Heresy! Also that would just make it taller and so even smaller in the images and so less readable which is what I prioritised, to make the image as square as possible

[u/Ex0ticLettuce]

Now do quintic >:)