Answer
.
Work Step by Step
Let $h\left( x \right)=f\left( x \right)g\left( x \right)$
A function f is an even function, if it satisfies $f\left( -x \right)=f\left( x \right)$.
Hence
$\begin{align}
& f\left( -x \right)=f\left( x \right) \\
& g\left( -x \right)=g\left( x \right) \\
\end{align}$
In order to find $h\left( -x \right)$:
$\begin{align}
& h\left( -x \right)=f\left( -x \right)g\left( -x \right) \\
& =f\left( x \right)g\left( x \right) \\
& =h\left( x \right)
\end{align}$
Since $h\left( -x \right)=h\left( x \right)$, it is an even function.
Thus,
$f\left( x \right)g\left( x \right)$ is an even function.
The product of two even functions f and g is even $f\left( -x \right)g\left( -x \right)=f\left( x \right)g\left( x \right)$.
