find the domain

Question

An open box can be made from a rectangular piece of cardboard by cutting a square of length x from each corner and bending up the sides. See the figure below. If the cardboard measures a = 24 cm by b = 30 cm, then the volume of the resulting box is given by

V(x) = x(24 − 2x)(30 − 2x).

What is the domain of the function V? (Assume that the volume must be greater than 0. Enter your answer using interval notation.)

I already tried with (-∞,∞), (0,12)U(15,∞), and [0,12]U[15,∞) but it says my answer is incorrect.

Answer 1

domain is (0,12) (without any Union to any other interval)

0<x<12 measured in cm

If x is less 0 or less the box has no volume

if x is greater than 12, the box has no volume or a "negative" volume. .