What is the range of the given function with a specified domain?

Norm850
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Homework Statement



Given the function, state the domain and range. I just want to make sure my notation is correct? More specifically, the I am f, can you have the independent variable in there?

Here's my answer: http://tinypic.com/r/2nlda2q/5



Homework Equations





The Attempt at a Solution

 
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Norm850 said:

Homework Statement



Given the function, state the domain and range. I just want to make sure my notation is correct? More specifically, the I am f, can you have the independent variable in there?

Here's my answer: http://tinypic.com/r/2nlda2q/5



Homework Equations





The Attempt at a Solution

Your image is just barely legible. Instead of drawing a crude sketch of the problem, and then uploading an image of it, why not just type the problem in here?

For your problem, the domain is fine, but the range is not. All you have done is just restate the equation of the function. If the domain is the set of integers, what set do you get for the range? It might be helpful to check a few pairs of numbers.
 
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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