How Can I Resolve My Confusion with a Tough Question?

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I am really confused:confused: with this question =|
Any help is greatly appreciated! Thanks!:smile:




http://answerboard.cramster.com/other-topic-5-311862-0.aspx"
 
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Pick a concrete example of a function (hint: you'll need on that is not 1-1). How about f(x)=x^2? Can you suggest sets A and F where f(A/F) is not equal to f(A)/f(F)?
 
Thanks!

Thank you to the infinite power for the help!
 
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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