Find an upper and lower bound for the reciprocal of the modulus of if

Out of all the the ways to break modulus how do I know which structure of the triangle inequalities to use?

Why am I getting the same value for my upper and lower bounds?

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- Sep 4th 2010, 10:10 AMdwsmithUpper and Lower Bounds
Find an upper and lower bound for the reciprocal of the modulus of if

Out of all the the ways to break modulus how do I know which structure of the triangle inequalities to use?

Why am I getting the same value for my upper and lower bounds? - Sep 4th 2010, 12:01 PMHallsofIvy
It is not necessary to do that. A is an upper bound for 1/f(x) if and only if 1/A is a lower bound (not 0) for f(x) and B is a lower bound for 1/f(x) if and only if 1/B is an upper bound for f(x).

- Sep 4th 2010, 12:04 PMdwsmith
I don't understand since the bounds are