f(x+y)+f(x-y)=F(xy)

Solution for f(x+y)+f(x-y)=F(xy) equation:

Simplifying
f(x + y) + f(x + -1y) = F(xy)
(x * f + y * f) + f(x + -1y) = F(xy)
(fx + fy) + f(x + -1y) = F(xy)
fx + fy + (x * f + -1y * f) = F(xy)
fx + fy + (fx + -1fy) = F(xy)

Reorder the terms:
fx + fx + fy + -1fy = F(xy)

Combine like terms: fx + fx = 2fx
2fx + fy + -1fy = F(xy)

Combine like terms: fy + -1fy = 0
2fx + 0 = F(xy)
2fx = F(xy)

Multiply F * xy
2fx = xyF

Solving
2fx = xyF

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by '2x'.
f = 0.5yF

Simplifying
f = 0.5yF