Question 164427
First, let's find the inverse. 
To find the inverse, first change to x,y notation.
{{{y=-sqrt(x)+2)}}}
Then interchange the positions of x and y and solve for y.
{{{highlight(x)=-sqrt(highlight(y))+2}}}
{{{x-2=-sqrt(y)}}}
{{{y=(x-2)^2}}}
The solution for the new y is the inverse function.
{{{f^(-1)(x)=(x-2)^2}}}
The domain for the inverse looks like all x, ({{{-infinity}}},{{{infinity}}}).
However, the domain of the original function is bounded by ({{{0}}},{{{infinity}}}) due to the square root function. 
The range of the original function is then ({{{-infinity}}},{{{2}}}).
The domain of the inverse must match the range of the original function.
Therefore the domain of the inverse function is ({{{-infinity}}},{{{2}}}).