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Answer the question based on the information given below:

Let x and y be real numbers and let

$f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$

Which of the following statements is true?

  1. $F(f(x,y)) .G(f(x,y)) = -F(f(x,y)).G(f(x,y))$
  2. $F(f(x,y)) .G(f(x,y)) > -F(f(x,y)).G(f(x,y))$
  3. $F(f(x,y)) .G(f(x,y)) \neq G(f(x,y)).F(f(x,y))$
  4. $F(f(x,y)) +G(f(x,y)) + f(x,y)= f(-x,-y)$
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G(f(x,y))=-F(f(x,y))=f(x+y)=|x+y|

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

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