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Algebra Level 3

If f(x)=xxf(x) = x|x|, then f1(x)f^{-1}(x) is equal to?

Clarification:

sgn(x)\text{sgn}(x) is the signum function defined as sgn(x)={1,x>00,x=01  ,x<0\text{sgn}(x)=\begin{cases} 1 \quad , x >0 \\ 0 \quad , x=0 \\ -1 \ \ , x<0 \end{cases} .

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