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

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.