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Mock AIME 3 Pre 2005 Problems/Problem 3

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$3.$ 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 $S$.

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