How many \(x\)?

Algebra Level 3

\[ f(x) = \dfrac{1}{x^{1000}} + \dfrac{1}{x^{999}} +\cdots + \dfrac{1}{x} + 1 + x + x^2 + \cdots + x^{999} + x^{1000} \]

Consider the above function for all real positive \(x\). Find the minimum value of \(f(x) \).

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