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Let 

\(f(x) = \begin{cases} k(x) &\text{if }x>0, \\ -\frac1{2x}&\text{if }x< 0\\ 0&\text{if }x=0. \end{cases}\)

Find the function \(k(x)\) such that \(f(x)\) is its own inverse function.

 Aug 21, 2022
 #1
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k(x) = x/2.

 Oct 7, 2022

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