Consider the functions defined by \( f, g: \mathbb{R} \rightarrow \mathbb{R} \) \( f(x)=x^{2}+\f...

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Consider the functions defined by \( f, g: \mathbb{R} \rightarrow \mathbb{R} \) \( f(x)=x^{2}+\frac{5}{12} \) and \( g(x)=\left\{\begin{array}{cc}2\left(1-\frac{4|x|}{3}\right) & |x| \leq \frac{3}{4} \\ 0, & |x|\frac{3}{4}\end{array}\right. \) If \( \alpha \) is the area of the region \( \left\{(x, y) \in \mathbb{R} \rightarrow \mathbb{R}:|x| \leq \frac{3}{4}, 0 \leq y \leq \min \{f(x), g(x)\}\right\} \) then the value of \( 9 a \) is
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