# It's beautiful!

Algebra Level 3

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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