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MathNet 2014 Question 24

Math Olympiad Vault · MathNet 2014

Question 24

Let $f$ be a function defined on nonzero real numbers such that for any nonzero $x$, $$
\frac{2}{x}f(-x) + f\left(\frac{1}{x}\right) = x.
$$ Find the value of $f(8)$.