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

Thread starter mtayab1994
Start date Nov 1, 2011
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Function Polynomial

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The discussion focuses on solving the polynomial function f(x) = sqrt(x^2 + 1) - |x| for values of x within the range 0 < |x| ≤ 1/2. The user attempted to find an inverse function by selecting a y value from the interval (0, 1] and solving the inequality 0 < sqrt(x^2 + 1) - |x| ≤ 1. However, they concluded with the incorrect result of 0 < |x| ≤ 1/2. The conversation highlights the need for a correct approach to solving the inequality and invites others to share their methods. Overall, the thread emphasizes the importance of verifying calculations in polynomial function problems.

Nov 1, 2011

mtayab1994

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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Nov 1, 2011

micromass

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No it is not correct. What is your work??

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