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# How to find inverse of own function?

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$f(x) = \begin{cases} k(x) &\text{if }x>3, \\ x^2-6x+12&\text{if }x\leq3. \end{cases}$

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

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I found inverse of $x^2 - 6x + 12$ as $3 \pm \sqrt{x - 3}$, but will that make the function inverse of itself? Hints appreciated.

May 23, 2021

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Since you want f(x) to be its own inverse, k(x) = x^2 - 6x + 12.

May 23, 2021
#2
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What!? No way... I dont think that is the right answer... The inverse of a function that is itself can't be itself! :P

Do you have a better idea? :)

May 24, 2021
#3
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AHHHHH

How do you find the inverse of its own function???

May 26, 2021