Question 828853
Not really have an inverse.  the inverse relation is not a function, but a relation.

{{{x=(y-3)^2+4}}}, switching x and y.
{{{(y-3)^2=x-4}}}
{{{y-3=0+- sqrt(x-4)}}}
{{{y=3+- sqrt(x-4)}}}  Composed of upper and lower branches.


The given equation, {{{y=(x-3)^2+4}}}, has vertex (3,4).
The domain of (-oo,3]  will have the LOWER branch, {{{y=3-sqrt(x-4)}}} as its inverse function.
The part of the domain, [3,oo) of the given function will have the UPPER branch, {{{y=3+sqrt(x-4)}}} as its inverse function.