Finding the Inverse of a Function - Attempting to Solve

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Homework Statement


JJDoR.png

Find the inverse

The Attempt at a Solution


Swapping x and y led me to nowhere. I'm really not sure where to go with this one, and a search online only led to simple problems where the previously mentioned method works.
 
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Perform long division and then try swapping x and y again.
 
I guess "inverse" means "inverse function". If y=f(x) then x=f^{-1}(y). f^{-1} is the inverse function. Can you express x in terms of y? You will have to solve some equation ...
If you plot your function with x horizontal and y vertical, and then rotate your plot by 90 degrees so that y is horizontal - you will see the plot of f^{-1}. Now, calculate...
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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