Mock AIME 3 Pre 2005 Problems/Problem 3

Problem

A function $f(x)$ is defined for all real numbers $x$ . For all non-zero values $x$ , we have

$2f\left(x\right) + f\left(\frac{1}{x}\right) = 5x + 4$

Let $S$ denote the sum of all of the values of $x$ for which $f(x) = 2004$ . Compute the integer nearest to $S$ .

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Mock AIME 3 Pre 2005 (Problems, Source)
Preceded by Problem 2	Followed by Problem 4
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