Let
\[f(x) = \begin{cases} k(x) &\text{if }x>2, \\ 2+(x-2)^2&\text{if }x\leq2. \end{cases} \]
Find the function $k(x)$ such that $f$ is its own inverse.
Since we want k(x) to be its own inverse, k(x) = 2 + (x - 2)^2 = x^2 - 4x + 6.
+230 
