Semicircle g has center at (-4,0) and radius 2.
Use the general equation for a circle:
(x-h)^2 + (y-k)^2 = r^2
Here, the center is (h,k), where h = -4 and k=0. Also, r = 2
So we have (x-[-4])^2 + (y-0)^2 = r^2 = 4
Let's solve for y in terms of x:
y^2 = 4 - (x+4)^2
Since we are interested in only the bottom half of this circle,
y = - sqrt(4 - x^2 - 8x - 16)