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

Sorry for repost, but Guest got it wrong... (No offence to guest, I greatly appreciate him/her attempt to help)

Jul 4, 2020

#1
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We have $$k(x) = 3 - \sqrt{x-3}$$

Obtain by solving the quadratic $$x=k^2-6k+12$$ for k and choosing the branch that is a reflection of $$x^2-6x+12$$ in the line y = x.

Jul 4, 2020
#2
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thank you somuch

Jul 4, 2020