Functions, with inequality

Algebra Level 2

It is given that \(f(x)\) is a function defined on \(R\), satisfying \(f(1)=1\), and for any \(x\in R\),

\(f(x+5)\geq f(x)+5\)

\(f(x+1)\leq f(x)+1\)

If \(g(x)=f(x)+1-x\), what is the value of \(g(2014)\)?

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