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# A y-intercept of f(x)

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.

Note by Daniel Liu
4 years, 3 months ago

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

Replace $$x$$ by $$\frac{2}{x}$$,

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

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

- 4 years, 3 months ago