Spicing up food production about stareater HOT 3 CLOSED

After some thinking and experimenting I've finally found the function that fits 
the bill (limit when x -> inf = constant, integral has inverse, etc.):

f(x) = a + b/(x+1)^2

where
x - dropoff distance (see below)
f(x) - food per farmer at dropoff distance of x
a - minimal food per farmer
b - maximal food per farmer minus "a"

Let's denotate with D population that can work as farmers without penalty. D + 
1st farmer has dropoff distance of 1/D, D + 2nd has distance of 2/D, etc. Now, 
how to calculate number of necessary farmers (excluding first D farmers)? Well, 
that's why I was looking for inverse of integral function.

Integral (with condition F(0) = 0) of the function above is 

F(x) = ax + b/(x+1) + b

Inverse of that integral is

F^-1(y) = (sqrt(g^2 + 4ay) + g) / 2a

where
y - food units demand (excluding demand covered by first D farmers) divided by D
g = y - a - b
a, b - same as above

Forumal correction:

F(x) = ax - b/(x+1) + b

F^-1(y) = (sqrt(g^2 + 4ay) + g) / 2a
where
y - food units demand (excluding demand covered by first D farmers) divided by D
g = a + b - y
a, b, x, D - same as above