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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 such that is its own inverse function.

 Dec 28, 2021
 #1
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Easy!  Take k(x) = -2x.

 Dec 28, 2021

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