Example 11. Find the domain of the function

\[
f(x)=\log \left(4-x^{2}\right)
\]
Solution. The logarithmic function is defined for positive values of its argument, i.e., for $4-x^{2}>0$, from which $x^{2}<4$ or $|x|<2$. Therefore, the given function is defined for $-2<x<2$, i.e., in the interval $(-2,2)$.