Soru

For any real number $x$, the custom unary operation $\triangle$ is defined by $\triangle(x) = 2x - x^2$. For all real numbers $u$ and $v$, the custom binary operation $\odot$ is defined by $u \odot v = \triangle(u) + \triangle(v) + uv$. The function $f$ is defined for all real numbers $x$ by $f(x) = x \odot (3 - x)$. What is the maximum value of $f(x)$?