Find the Domain of f(x) = cos-1(x) + cos(x)
Solution:
Given function:
\[ f(x) = \cos^{-1}(x) + \cos(x) \]
Step 1: Domain of cos-1(x)
\[ -1 \leq x \leq 1 \]
Step 2: Domain of cos(x)
\[ \cos(x) \text{ is defined for all real numbers} \]
Step 3: Intersection of domains
\[ [-1,1] \cap \mathbb{R} = [-1,1] \]
Final Answer:
Domain = \[ [-1,1] \]