y = -(1/2) sqrt(x + 3) Interchange the x and y
x = -(1/2) sqrt(y + 3) multiply through by - 2
-2x = sqrt(y + 3) Square both sides.
(-2x)^2 = (sqrt(y + 3))^2
4x^2 = y + 3 Subtract 3 from both sides.
y = 4x^2 - 3
The usual rule is to interchange the domain and range of the original equation with the inverse. The range of the original equation is 0 => y > -infinity.
If that is the case, then the domain of the inverse is 0<=x. The graph was revised and provided by Mathmate. It is the correct way to represent this function and it's inverse Including the fact that x<=0. That restriction is very important. The line is x = y and the graphs should reflect around that line.
