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.

Easy Math Editor

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Comments

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

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

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

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

jatin yadav - 7 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$