there are three f(x), make comparisons between each to get the relative division in the real line x.
1) 1/x < 2x ==> (x>1/sqrt(2))
2) 1/x < x^2 ==> (x>1)
3) 2x < x^2 ==> (x>2)
so you have possibilities of changes
(0, 1/sqrt(2)) ==> get order from above comparison results.
This is interesting. Never seen it solved this way. So, after you have found the relative divisions, what do you do with them that would help you figure out the ones (I, II, or III) that could work. You're a pretty smart guy/lady, but please break this down as simple as possible.