Let \(f(x) = \begin{cases} k(x) &\text{if }x>3, \\ x^2-6x+12&\text{if }x\leq3. \end{cases} \) , find k(x) such that f is it's own inverse.
When \(x\leq 3, x^2-6x+12=(x-3)^2+3.\) So we want \(k(x^2-6x+12)=(x-3)^2+3 \text{ for } x\leq3.\) I'm not sure how to continue. Thank you in advance for your help.
