Interchange the x and y and solve for the resulting y.
x = 4y^2 - 2
(x + 2) = 4y^2
(x + 2)/4 = y^2
+/- sqrt(x + 2)/2 = y
The graph of these two is below.
The original is in red
The inverse is in blue and green
x = 4y^2 - 2
(x + 2) = 4y^2
(x + 2)/4 = y^2
+/- sqrt(x + 2)/2 = y
The graph of these two is below.
The original is in red
The inverse is in blue and green