By cutting away an $\backslash ($ x $\backslash )-$by$-\backslash ($ x $\backslash )$ square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed.

If the piece of cardboard is $48$ inches long by $34$ inches wide, find a function in the variable $\backslash ($ x $\backslash )$ giving the volume of the resulting box.

Volume, as a function of $\backslash ($ x$=\backslash )$

Determine the domain of the function for volume. Enter your answer using interval notation.

Domain of the function for volume $\backslash (=\backslash )$