Final answer:
The formula for the surface area of the box with a square base can be expressed as SA = 2x³ + 4x² m². The domain of the surface area function is (0,[infinity]), meaning the side length of the base cannot be negative or zero and can be any positive value up to infinity.
Step-by-step explanation:
To find a formula for the surface area of the rectangular box, we need to first find the dimensions of the box. Since the volume of the box is given as 9 m³ and the base is square, we can find the length of the side of the base by finding the square root of the volume, which is √9 = 3 m.
The formula for the surface area of an open rectangular box is SA = 2lw + 2lh + lw, where l is the length, w is the width, and h is the height of the box.
Since the base is square, the length and width are both equal to x. So substituting x for l and w, the formula for the surface area becomes SA = 2x³ + 4x² m².
The domain of the surface area function is (0,[infinity]). This means that the length of a side of the base cannot be negative or zero, and it can be any positive value up to infinity.