Consider the functions \( f,g:\mathbb{R}\to\mathbb{R} \) defined by
If \( \alpha \) is the area of the region \( \Big\{(x,y)\in\mathbb{R}\times\mathbb{R}:|x|\le \dfrac{3}{4},\,0\le y\le \min\{f(x),g(x)\}\Big\} \), then the value of \( 9\alpha \) is ________________.
