Question 850038
Quick way,

{{{x=-sqrt(y+5)+3}}}, roles of x and y were switched. y represents the original f(x), a representation only.
{{{x-3=-sqrt(y+5)}}}
{{{x^2-6x+9=y+5}}}
{{{y=x^2-6x+9-5}}}
{{{highlight_green(y=x^2-6x+4)}}}


That is not yet finished.  You need to know the vertex, because f(x) was the lower half of a parabola, so the inverse must correspond to that lower half.


Put into standard form.
{{{y=x^2-6x +(6/2)^2-(6/2)^2+4}}}-----Completing the Square
{{{y=(x-3)^2+4-9}}}
{{{highlight(y=(x-3)^2-5)}}}-------vertex is (3,-5)

We must include the restriction, {{{highlight(x<=3)}}}.