Final answer:
The domain of p(x) is [0, 20] assuming p(x) is the same as the provided f(x). The domain of g(x) is (-∞, ∞) since it's a constant function. The domain of composite functions p(g(x)) and g(p(x)) both would be [0, 20], considering the output of g(x) and the input range of p(x).
Step-by-step explanation:
When looking at the domains for the given functions, we need to consider what inputs are valid for each function. This includes understanding that domain refers to the set of all possible x-values which will make the function 'work' and will output real y-values.
For function p(x), you mentioned that p(2) is given, but no function definition for p(x) is provided. However, since there is mention of f(x) as a horizontal line for 0 ≤ x ≤ 20, I'll assume this is actually meant to be p(x) and will proceed on that basis:
- The domain of p(x), which I assume is the function f(x) described as a horizontal line between 0 ≤ x ≤ 20, would be the interval [0, 20].
- The domain of g(x) = 22 - 4, which is a constant, would technically be all real numbers, represented by the interval (-∞, ∞).
- For p(g(x)), since g(x) outputs a constant, and p(x) can take any real number from 0 to 20, the domain remains the same as p(x), which is [0, 20].
- For g(p(x)), since g(x) takes any real number as input, and p(x) only outputs values in the interval [0, 20], g(p(x)) has the domain [0, 20] as well.