# Interesting Function

Calculus Level 4

Given a function $$\large{f:\mathbb{R}\to\mathbb{R}}$$ which satisfies:

$\large{f(x)+f(y)=f(\frac{x+y}{1-xy})}$ $$\forall x,y \in\mathbb{R}$$

also, $$\large{\lim\limits_{x\to 0}\frac{f(x)}{x}=2}$$

FIND the value of $$\large{f(\frac{1}{\sqrt{3}})=a}$$

ALSO FIND the value of $$\large{f'(1)=b}$$

ENTER YOUR ANSWER AS $$\large{a+b}$$

Answer upto $$\text{5 decimal places}$$.

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