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

[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?

 

[micromass]

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