y = f(x) = sqrt(8 - 4x) - 2
Domain: 8 - 4x >= 0, x <= 2. Range: y >= -2.
To find inverse of f, change all x's to y's and all y's to x's:
x = sqrt(8 - 4y) - 2; Range: 8 - 4y >= 0, y <= 2; Domain: x >= -2
x + 2 = sqrt(8 - 4y)
(x + 2)^2 = 8 - 4y, x >= -2
y = f^{-1}(x) = 2 - (1/4)*(x + 2)^2, x >= -2.