Which of the following statements is true?

f(x,y) = |x+y|

F(f(x,y)) = -f(x,y) = -|x+y|

G(f(x,y)) = -F(f(x,y)) = |x+y|

Option A: F(f(x, y)) . G(f(x, y)) = -F(f(x, y)) . G(f(x, y))  =>LHS = -|x+y|$$^2$$, RHS = |x+y|$$^2$$  Hence false.

Option B: F(f(x, y)) . G(f(x, y)) > -F(f(x, y)) . G(f(x, y)), Since, LHS is smaller than RHS. False

Option C: F(f(x, y)) . G(f(x, y)) $$\neq $$ G(f(x, y)) . F(f(.x, y)), Here LHS=RHS. Hence false.

Option D:

=> G(f(x,y)) + F(f(x,y)) = 0

f(x,y) = f(-x,-y)

=> G(f(x,y)) + F(f(x,y)) + f(x,y) = f(-x.-y)