Let \(f(x) = \begin{cases} k(x) &\text{if }x>3, \\ x^2-6x+12&\text{if }x\leq3. \end{cases}\) Find the function \(k(x)\) such that \(f\) is its own inverse.
We want f(x) to be its own inverse, so k(x) = x^2 - 6x + 12.
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