Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration,C, in mg/L, of a particular medication after being injected into a patient can be given by the functionC(t)= -18t^2 +54t / t^2 + 7t + 10 where the time,tis hours after injection.

What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations.