Fun with Functions!

Algebra Level 4

Let \(f: \mathbb {R \to R} \) such that:

\[\begin{cases} f(1)=1 \\ f(x+5) \ge f(x)+5 \\ f(x+1) \le f(x)+1 \end {cases} \]

Let \(g(x)=f(x)+1-x\). Then find \(g(2002)\).


Source: This is a problem from the China Mathematics Competition (2002).
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