If $f(x) = x|x|$, then $f^{-1}(x)$ is equal to?

**Clarification:**

$\text{sgn}(x)$ is the signum function defined as $\text{sgn}(x)=\begin{cases} 1 \quad , x >0 \\ 0 \quad , x=0 \\ -1 \ \ , x<0 \end{cases}$.

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