Many Greatest Integers!

Algebra Level 4

Let \(\large f(x) = e^{x^2-4} + \lfloor e^{2x} \rfloor + \lfloor e^{-2x} \rfloor \).

What are the values of \(x\) satisfying \( \lfloor f(x) \rfloor + \lfloor -f(x) \rfloor = 0 \)?

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