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A Function

Source: 2002 National High School Mathematics League, Exam One, Problem 10

March 16, 2020
function

Problem Statement

f(x)f(x) is a function defined on R\mathbb{R}. f(1)=1f(1)=1, and for all x∈Rx\in\mathbb{R}, f(x+5)≥x+5,f(x+1)≤f(x)+1f(x+5)\geq x+5,f(x+1)\leq f(x)+1. If g(x)=f(x)+1−xg(x)=f(x)+1-x, then g(2002)=g(2002)=________.
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