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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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