Given functions $f$ and $g$, determine the domain of $f+g$. \[ f(x)=3 x-4, \quad g(x)=5 x+3 \] (A), -3$)$ or $(-3$, 10, (B) ) (- (C) , 0) or $(0$, ) $(-$ (D). )

Step 1 ：Given functions $f$ and $g$, determine the domain of $f+g$. \[f(x)=3 x-4, \quad g(x)=5 x+3\]

Step 2 ：To find the domain of $f+g$, we need to find the domain of each function and then find the intersection of their domains.

Step 3 ：The domain of a linear function like $f(x) = 3x - 4$ and $g(x) = 5x + 3$ is all real numbers. So, the domain of both functions is $(-\infty, \infty)$.

Step 4 ：Since the domain of both functions is all real numbers, the domain of $f+g$ will also be all real numbers.

Step 5 ：\(\boxed{(-\infty, \infty)}\)