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# Picewised Defined Function, Finding the inverse of f(x)

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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.

Aug 5, 2020