Consider the function $g(x) = x^2 - 2x+3$ on the domain $D = (1,3)$.
Determine a suitable codomain $C$ so that the function has an inverse function and find the inverse function.
I've already found the codomain but I'm struggling to find the inverse. Do I have to complete the square? I have no idea how I'm supposed to do it with this sort of question. Am I completely wrong? Should I be trying to apply some other formula?
HINT
Let use quadratic formula.
$$y= x^2 - 2x+3 \implies x^2 - 2x+3-y=0\implies x=...$$
or as an alternative
$$y= x^2 - 2x+3 =(x-1)^2+2\implies (x-1)^2=y-2 \implies x=...$$