Final answer:
The explicitly calculated product (f.g)(x) for the functions f(x) = 2x and g(x) = 32 would be 64x, which is not among the provided choices. There is also a discrepancy in the function notation as (f.g)(x) suggests multiplication while (f∘g)(x) suggests composition; neither approach with the provided options leads to a correct answer from the choices given.
Step-by-step explanation:
To find the product of the functions f(x) and g(x), denoted as (f.g)(x), you need to multiply the outputs of f and g for the same input value x. Since f(x) = 2x and g(x) = 32, (f.g)(x) is calculated by multiplying the two expressions together.
Therefore, (f.g)(x) = f(x) × g(x) = (2x) × 32 = 64x.
However, since the choices provided do not include 64x, and the question refers to (f∘g)(x) which could be interpreted as function composition rather than multiplication, let's also consider (f∘g)(x) = f(g(x)). Since g(x) is 32 (which is a constant and not dependent on x), f(g(x)) = f(32) which is 2 × 32 = 64. But again, this option is not available in the choices. If we assumed a typo in the question and (f.g)(x) was intended as (f∘g)(x), then option D (f∘g)(x) = 8x would appear to be the closest match, but that is an assumption not directly supported by the information provided.
Since none of the provided choices are correct based on the explicit functions given, and we have an apparent discrepancy in the function notation (product versus composition), it would be advisable to double-check the question for clarity or seek additional information.