Let $R$ be the triangular region with corner points $(0,0), (3,0)$ and $(0,3)$. Find $g(u)$ if $\displaystyle \int\!\!\int_{R} f(6 x + 6 y) \: dA = \displaystyle \int_0^{18}f(u) g(u) \: du$.

$g(u) =$