\left\{ \begin{array} { l } { y = - z ^ { 2 } - 2 z + 3 + | 3 z - 4 | } \\ { - 3 < z < 1 } \end{array} \right.
Solve for y
y=\frac{-\left(2z+5\right)^{2}+53}{4}
z>-3\text{ and }z<1
Solve for z
\left\{\begin{matrix}z=\frac{\sqrt{53-4y}-5}{2}\text{, }&y>1\text{ and }y\leq \frac{53}{4}\\z=\frac{-\sqrt{53-4y}-5}{2}\text{, }&y>13\text{ and }y\leq \frac{53}{4}\end{matrix}\right.
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