1. (2 points) What is the domain of g(x) = arccos(x − 3)?A. (−∞, ∞)B. [−1, 1]C. [−4, −2]D. (−4, −2)E. [2, 4]

The domain of a function is the set of all possible input values (often denoted as 'x' values) which will output real numbers.

The arccos function, also known as the inverse cosine function, has a domain of [-1, 1]. This means that the input of the arccos function must be between -1 and 1, inclusive.

In the function g(x) = arccos(x - 3), the input to the arccos function is (x - 3). Therefore, to find the domain of g(x), we need to find all values of x that make (x - 3) fall within the interval [-1, 1].

We can set up the following inequalities to find these values:

-1 ≤ x - 3 ≤ 1

Adding 3 to all parts of the inequality gives:

2 ≤ x ≤ 4

Therefore, the domain of g(x) = arccos(x - 3) is [2, 4]. So, the correct answer is E. [2, 4].