A function \(f\) satisfies \(17f(x)+65f\left(\dfrac{2}{x}\right)=257\) and is continuous at \(x=0\). This function is known to have a y-intercept of \((0,\dfrac{a}{b})\), where \(a,b\) are relatively prime integers and \(b\ne 0\). What is \(a+b\)?

This was my failed submission to brilliant.org. I'm guessing that it doesn't really fit into any of the categories.

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TopNewest\(17f(x) + 65f(\frac{2}{x}) = 257\)

Replace \(x\) by \(\frac{2}{x}\),

\(17f(\frac{2}{x}) + 65 f(x) = 257\)

Solve to get \(f(x) = \frac{257}{82} \) always , Hence \(\frac{a}{b} = \frac{257}{82}\) \(\Rightarrow a + b = \fbox{339}\)

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