# 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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