# How many $$x$$?

Algebra Level 4

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

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

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