[tex]\it x\circ y = 3x+3y-xy-6 =3x+3y-xy-9+3 =
\\ \\
= (3x-9)-(xy-3y )+3 = 3(x-3) -y(x-3) +3 =
\\ \\
= (x-3)(3-y) +3 = 3-(x-3)(y-3)\ \ \ \ (*)[/tex]
[tex]\it x\ \textless \ 3 \Rightarrow x-3\ \textless \ 0 \ \ \ \ (1)
\\ \\
y\ \textless \ 3 \Rightarrow y-3\ \textless \ 0 \ \ \ \ (2)
\\ \\
(1), (2) \Rightarrow (x-3)(y-3)\ \textgreater \ 0 |_{\cdot(-1)} \Rightarrow -(x-3)(y-3)\ \textless \ 0|_{+3} \Rightarrow
\\ \\
\Rightarrow 3-(x-3)(y-3) \ \textless \ 3 \Rightarrow 3-(x-3)(y-3) \in (-\infty,\ 3) \ \ \ \ (**) [/tex]
[tex]\it (*),(**) \Rightarrow x\circ y \in(-\infty,\ 3) [/tex]
