Question

How do I find the inverse function of $$f(x)=x^5+x$$

Answer 1

The standard method is to replace the f(x) with a x and each x with a y. Then, solve for y. However, it seems like this would be a bit messy in this case... still thinking here.

Answer 2

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Yeah I don't think this will work well

Answer 3

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

Answer 4

Yeah this is my question haha.

Answer 5

Obviously, I just said that because if we only need the graph, we can just reflect over y = x and obtain the visual solution. :)

Answer 6

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

Answer 7

agreed

Answer 8

We can invent a new function and call it the freckles function where the freckles function is the inverse function of f(x)=x^5+x.
I guess that is what Lambert did.

Answer 9

LOL

Answer 10

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

Answer 11

hahaha :)

Answer 12

how about polar coords

Answer 13

I like what @freckles is saying but I'm not sure if I like this answer I want something more algebraic.

Answer 14

what we're looking for is a way to write out the inverse function with one equation without having to deal with the +/- sqrts right

Answer 15

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

Answer 16

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

Answer 17

@Empty do you have an answer and are challenging us, or is this something you wanted to explore with us while challenging yourself and us?

Answer 18

@freckles probably the second option