# Find the domain of f(x)

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 $\mathrm{R} \cap[-1,1]=[-1,1]$.