Answer
$(0,\infty)$
Work Step by Step
The domain of $\textbf{F}(t)-\textbf{G}(t)$ is the intersection of the domains of $\textbf{F}(t)$ and $\textbf{G}(t)$, since it is defined only if both $\textbf{F}(t)$ and $\textbf{G}(t)$ are defined. For the domain of $\textbf{F}(t)$, polynomial functions are defined in $(-\infty,\infty)$ and $\ln x$ is defined in $(0,\infty)$ so the intersection of these domains is $(0,\infty)$. For the domain of $\textbf{G}(t)$, all components are polynomials, so the intersection of the domains is $(-\infty,\infty)$. Thus, the domain of $\textbf{F}(t)-\textbf{G}(t)$ is the intersection of $(-\infty,\infty)$ and $(0,\infty)$ which is $(0,\infty)$.
