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And I'm assuming the question is to find the actual equation of the inverse correct?

Yeah this is my question haha.

Hey quick question, so this function is 1 - 1 right

agreed

LOL

Clearly, the inverse does exist, so we can call it whatever we want right? :)

hahaha :)

how about polar coords

Is there a way to do it with +/- sqrts?

i dunno i didnt really do anything i just saw it had powers in it so lol

|dw:1438056301096:dw|

how about defining inversions in terms of a matrix transformation

making a transformation*

we did talk about how numbers are weak matrices

so why dont variables and functions

hmm if i were to ask you
what is the inverse of
Y=f(x,z)

id think of more dimensions then, why consider more dimensions for 2 variables only

oops forgot the 5

\[5x^4+1=\frac{1}{f'(x^5+x)}\]

I don't know. I thought it was worth investigating @Astrophysics

so by the way for the inverse of *
z=f(x,y) would we reflect across z+x+y=0 plane or somethingÃ‰

though you wind up with f(u)=x+C
where u=x^5+x
so we are kind of where we started

i think complex numbers and complex functions can be a nice way to deal with these reflections

Oh to add to that, \[f(a) = b \implies f^{-1}f(a) = f^{-1}(b) \implies a = f^{-1}(b)\]

like conjugating automatically reflects across the horizontal

So, we would need to take a + bi to b + ai to perform the equivalent reflection.

yeah

Well, if you want to get fancy! ... lol exactly!

That is actually a really neat representation. :)

Yeah I did the same thing didn't understand it haha

whoa...

I have never seen that before. Maybe wolfram gave up.

Yeah same here hahaha

Wolfram is like "I'll put these fake plus signs on them and not explain them shhhhhhhhhhhhhh"

The Root[stuff, 3] indicates that this is a third root however.

I have nothing to say about the "&" though... :P

how did wolfram get the graph :/

you very wise

Getting the graph is easy enough as long as it is smart enough to plug in y's first instead of x's.

ah ok :)

seems legit to me

wow that is totally cute in a cute infinite way

ty! <3