Is \(f\) a additive function?

Algebra Level 5

Let \(f:[0,1]→R\) be a continuous function such that

\(f(x_{1})+f(x_{2})+......+f(x_{1151})=1\) for all \(x_{1},x_{2},...,x_{1151}\) in \([0,1]\) which satisfy \(x_{1}+....+x_{1151}=1\).

Given that \(f(0)=7\), find \(f(\frac{1}{2014})\).

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