Functions, with inequality

Algebra Level 2

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

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

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

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

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