Answer
a. f and g
b. f and g
c. f and g, zero
Work Step by Step
a.
The function $(f+g)(x)=f(x)+g(x)$ is defined when both $f(x)$ and $g(x)$are defined,
meaning that x must be in the domains of both f and g.
b.
The function $(fg)(x)=f(x)\cdot g(x)$ is defined when both $f(x)$ and $g(x)$are defined,
meaning that x must be in the domains of both f and g.
c.
$(\displaystyle \frac{f}{g})(x)=\frac{f(x)}{g(x)}$ is defined when both $f(x)$ and $g(x)$are defined,
AND g(x) must not be zero,
meaning that x must be in the domains of both f and g, and $g(x)\neq 0.$
