Answer
See below
Work Step by Step
The domain of a function combined from functions $f$ and $g$ by addition, subtraction, multiplication and division is the intersection of the domains of f and g (for division, $f/g$ an additional condition is $g(x)\neq 0)$.
The domain of a real-valued function of a real variable is the subset of real numbers for which the function value can be calculated.
So, problems arise for x that yield zero in the denominator, that yield a negative radicand of an even root, or that yield a negative argument for a logarithmic function.
Example:
Let $f(x)=\ln(x+2)$ and $g(x)=\sqrt{9-x^{2}}$
The domain of f is $(-2, +\infty)$, as these numbers yield a positive argument of the logarithm.
The domain of g is $[-3,3]$, because outside this interval, the radicand is negative, and we can't calculate the square root.
So, the domain of $f+g,\quad f-g$ and $fg$ is the intersection of domains of f and g,
(the numbers x for which we can calculate both f(x) and g(x)):
$D=(-2,3]$
For, $f/g$ we exclude x=3 from this domain, as it would yield a zero in the denominator.
$D=(-2,3)$
