Solving Polynomial Functions: Find x in 0<|x|≤1/2

mtayab1994
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Homework Statement



f:ℝ→ℝ
x:→sqrt(x^2+1)-lxl

Homework Equations



calculate f^-1(]0,1])

The Attempt at a Solution



well i chose a y from ]0,1] and tried to find an x that solves the problem like the following.

0<sqrt(x^2+1)-lxl≤1

at the end i got the following: 0<lxl≤1/2 is my work correct?
 
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No it is not correct. What is your work??
 

Thread 'Finding the nth roots of a complex number'

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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