coding style – How to calculate how many points in function f are greater than the average of functions g and k?

Consider 3 functions f, g and k

Suppose we want to know all the three functions at all 400 points in the set

P={(x, y )|x=-1,-0.9,-0.8,-0.7….,1 and y=-1,-0.9,-0.8,-0.7….1

this is what i have so far

    Clear(f, x, y, g, k)
    f(x_, y_) := x^2+2*Sin(x*y)-2 
    g(x_, y_) := x*Cos(x+y)+8*y
    k(x_, y_) := (x^3 + y^3)/(x^3 + e^(y/200))
    p1 = Table(f(x, y), {x, -1, 0.9, 0.1}, {y, -1, 1, 0.1})

How can we calculate how many points in function f are greater than the average of functions g and k? Thank you