Question:
Find the domain of definition of $f(x)=\cos ^{-1}\left(x^{2}-4\right)$.
Solution:
For $\cos ^{-1}\left(x^{2}-4\right)$ to be defined
$-1 \leq x^{2}-4 \leq 1 \Rightarrow 3 \leq x^{2} \leq 5 \Rightarrow x \in[-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]$
Hence, the domain of $f(x)$ is $[-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]$.