Algebra and Trigonometry 10th Edition

Domain: $(0,8)$ or $0\lt x\lt8$
$x+2y-8=0$ $2y=8-x$ $y=4-\frac{x}{2}$ Since $A=xy$, we must have that $x\gt0$ and $y\gt0$. $y\gt0$ $4-\frac{x}{2}\gt0$ $-\frac{x}{2}\gt-4$ $\frac{x}{2}\lt4$ $x\lt8$ So, we must have that $x\gt0$ and $x\lt8$. That is, $0\lt x\lt8$.