inverse function

Let 

f(x)  = k(x) if x > 3

f(x) = (x - 3)^2 + 3 if x <= 3                                 x<=3,  y>3

Find k(x) such that f is it's own inverse.

y=(x - 3)^2 + 3

make x the subject

\(x=\pm\sqrt{y-3}+3\\ \text{For the inverse, swap x and y}\\ y=\pm\sqrt{x-3}+3 \qquad \\but \quad y\le3 \quad and \quad x>3\\ \text{ Since y is negative it must be the - sign}\\ y=-\sqrt{x-3}+3 \qquad where \qquad x>3 \)

so 

\(k(x)=-\sqrt{x-3}+3 \qquad where \qquad x>3\)