In the following, if your answer includes more than one interval write the intervals separated by the “union” symbol, $\cup$, which you can type as U. If you need to enter the $\infty$ symbol, type it as inf.
Given that $f(x)={x^{2}-2x}$ and $g(x)={x+12}$, find and simplify the following:
1. $\left(f+g\right)(x)={}$ and the domain of $\left(f+g\right)$ is
2. $\left(f-g\right)(x)={}$ and the domain of $\left(f-g\right)$ is
3. $\left(fg\right)(x)={}$ and the domain of $\left(fg\right)$ is
4. $\left(\frac{f}{g}\right)(x)={}$ and the domain of $\left(\frac{f}{g}\right)$ is