How does one simplify such a function?

Algebra Level 5

\[\large {f(2+x) = f(2-x) \\ f(7+x) = f(7-x)}\]

A function \(f\) is defined for all real numbers and, for all real \(x\), satisfies the two equations above.

If \(f(0)=0\), what is the smallest number of solutions that \(f(x) = 0\) could have in the interval \(-2000 \leq x \leq 2000\)?

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