1. Key Concepts for Domain of Functions

To determine the domain of a function, we must ensure that all mathematical operations within the function are well-defined. For this problem, we need to recall the domain restrictions for inverse trigonometric functions and logarithmic functions:

• Domain of $\cos^{-1}(u)$: The argument $u$ must satisfy $-1 \le u \le 1$. If $u$ falls outside this range, $\cos^{-1}(u)$ is undefined in real numbers.
• Domain of $\log_b(v)$: The argument $v$ must be strictly positive, i.e., $v > 0$. Additionally, the base $b$ must be positive and not equal to 1 ($b > 0, b \