Given the two functions $f$ and $g$, find $f+g$ and identify the domain.

$f\left(x\right)=11x^2-3x-7$, $g\left(x\right)=3x-4$

Given the two functions $f$ and $g$, find $fg$ and identify the domain.

$f\left(x\right)=\sqrt{x}$, $g\left(x\right)=x+17$