Mathematics - Functions Question with Solution | TestHub

$x+y=a,x-y=b\Rightarrow x=\frac{a+b}{2},y=\frac{a-b}{2}$

$$\begin{array}{rl}f(a,b)& =\left(\frac{a+b}{2}\right)\left(\frac{a-b}{2}\right)=\frac{a^2-b^2}{4}\\ A\cdot M& =\frac{f(x,y)+f(y,-x)}{2}=\frac{x^2-y^2+y^2-x^2}{4}=0\end{array}$$