Final answer:
The question deals with the composition of functions p(x) and g(x), resulting in p(g(x)) = -4x - 3 and g(p(x)) = -4x - 4. It also touches on the concepts of even and odd functions, which relate to their symmetry properties.
Step-by-step explanation:
The given question requires understanding the concept of the composition of functions, which means applying one function to the result of another. In the example provided, functions p and g are composed. For A) p(g(x)), we apply g(x) inside p(x), resulting in p(g(x)) = 2(-2x - 2) + 1 which simplifies to -4x - 4 + 1, or -4x - 3. For B) g(p(x)), we apply p(x) into g(x), which results in g(p(x)) = -2(2x + 1) - 2, simplifying to -4x - 2 - 2, or -4x - 4.
Regarding the details of even and odd functions, it's important to know that an even function is symmetric about the y-axis and an odd function, or anti-symmetric function, is symmetrically reflected about the y-axis and then the x-axis. If we multiply an even function by another even function or an odd function by another odd function, the product is an even function. These concepts relate to the symmetry properties of functions, which are fundamental in algebra and precalculus studies.