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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 step by step, we will follow the logical deductions and calculations based on the given functional equation and limit condition. ### Step 1: Understanding the Functional Equation We start with the functional equation given: \[ f(x) + f(y) = f\left(\frac{x+y}{1-xy}\right) \] for all \( x, y \in \mathbb{R} \) where \( xy \neq 1 \). ### Step 2: Substituting Values ...
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