$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.

---

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.

HighSchoolDx May 23, 2021

#2**+1 **

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? :)

HighSchoolDx May 24, 2021