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"If "f(x)+f(y)=f((x+y)/(1-xy))" for all ...

`"If "f(x)+f(y)=f((x+y)/(1-xy))" for all "x,y in R, (xyne1), and lim_(xrarr0)(f(x))/(x)=2" then find "f((1)/(sqrt(3))) and f'(1).`

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To solve the problem, we need to find the function \( f(x) \) that satisfies the given functional equation and limit condition. Let's go through the steps systematically. ### Step 1: Analyze the Functional Equation We are given the functional equation: \[ f(x) + f(y) = f\left(\frac{x+y}{1-xy}\right) \] for all \( x, y \in \mathbb{R} \) where \( xy \neq 1 \). ...
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