# The information is enough to get the function value

Calculus Level 4

$\large f(x+y)=\frac{f(x)+f(y)}{1-f(x)f(y)}$ The function $$f(x)$$ is defined for any value of $$x$$ in certain open interval centered at 0, and for any values of $$x$$ and $$y$$ in that interval the given functional equation is always valid. Additionally, $$\displaystyle \lim_{x\to 0} \frac{f(x)}{x}=2$$.

Find the approximate value of $$f(\frac{\pi}{12})$$ rounded to the nearest hundredth.

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