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avatar+176 

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
avatar+30915 
+3

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
avatar+176 
+2

thank you somuch

 Jul 4, 2020

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