For this question, take the range of \( \cot^{-1} x \) as \( \left( - \dfrac{\pi}{2}, \dfrac{\pi}{2} \right] \).

\[ \large f(x) = \dfrac{1}{\sqrt{\ln(\cot^{-1}x)}} \]

Find the domain of the function \(f(x)\) above.

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