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.
You can take k(x) = -2x.
