Answer
$\text{True}$
Work Step by Step
For functions $f$ and $g$, $(f.g)(x)=f(x).g(x)$
Thus, $(f.g)(x)$ is only defined for $x$-values for which both $f(x)$ and $g(x)$ are both defined.
This means that domain of $(f.g)(x)$ consists of the numbers $x$ that are in the domains of both $f$ and $g$.
Hence, the given statement is $\text{true}$.
