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If f(x)=x∣x∣f(x) = x|x|f(x)=x∣x∣, then f−1(x)f^{-1}(x)f−1(x) is equal to?
Clarification:
sgn(x)\text{sgn}(x)sgn(x) is the signum function defined as sgn(x)={1,x>00,x=0−1 ,x<0\text{sgn}(x)=\begin{cases} 1 \quad , x >0 \\ 0 \quad , x=0 \\ -1 \ \ , x<0 \end{cases} sgn(x)=⎩⎪⎨⎪⎧1,x>00,x=0−1 ,x<0.
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