Question: Find the domain of $f(x)=\cos ^{-1} x+\cos x$.
Solution:
For $\cos ^{-1} x$ to be defined.
$-1 \leq x \leq 1$
Now, $\cos x$ is defined for all real values.
So, domain of $\cos x$ is $\mathrm{R}$.
Domain of $f(x)$ is $\mathrm{R} \cap[-1,1]=[-1,1]$.
