If X is uniformly distributed on the interval (0, 12), then its PDF is
[tex]f_X(x) = \begin{cases}\frac1{12} & \text{if }0 < x < 12 \\ 0&\text{otherwise}\end{cases}[/tex]
or simply
[tex]f_X(x) = \dfrac1{12} \text{ where } 0 < x < 12[/tex]
and the zero-elsewhere case is assumed.
Whether you include 0 and 12 in the domain is irrelevant, since the probability that X = 0 or X = 12 are both zero.
