# 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 $$g(2002)$$.

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