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I want to ask a question about Reduce. I have a function, say f[x]. When I use the command Reduce[f[x] > 0, {x}], it gives me an interval for x. But, I don't want to have an interval. I want to have an upper bound for x.

For example: After the command Reduce[f[x] > 0, {x}], the output is a_1 < x < a_2. But I want to have only a_2. How can I get it?

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Make sure you use the correct "brackets", i.e. f(x) vs. f[x] – Pinguin Dirk Apr 14 '13 at 11:46
@ Pinguin Dirk, you are right. i refit it. – MATIRMAK Apr 14 '13 at 11:48
A direct answer would depend on the details of your f; for the example you made try Part[a1 < x < a2, -1]. – b.gatessucks Apr 14 '13 at 11:48
E.g. Reduce[27 > x^3 > 8, x] // Last yields 3. – Artes Apr 14 '13 at 12:30
Sometimes there just isn't an upperbound for x. Take for instance x^2-1>0. – Sjoerd C. de Vries Apr 14 '13 at 12:33

I'll assume that the question is simply how to take an inequality such as

interv = a1 < x < a2

and extract the upper limit from it. This could work:

Simplify[Max[List @@ interv], interv]

(* ==> a2 *)
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