Given functions $f$ and $g$, determine the domain of $f+g$. \[ f(x)=3 x^{2}+6, \quad g(x)=2 x^{3}-4 \]

Step 1 ：Given functions $f$ and $g$, determine the domain of $f+g$. \[f(x)=3 x^{2}+6, \quad g(x)=2 x^{3}-4\]

Step 2 ：Find the domain of $f(x)$ and $g(x)$.

Step 3 ：The domain of $f(x)$ is $(-\infty, \infty)$.

Step 4 ：The domain of $g(x)$ is $(-\infty, \infty)$.

Step 5 ：\(\boxed{\text{The domain of } f+g \text{ is } (-\infty, \infty)}\)