Final answer:
To find (gf)(x) with f(x) = 3x and g(x) = 2x, we compute g(f(x)) = g(3x) = 2×3x = 6x. The correct answer, 6x, is not listed among the provided choices, suggesting an error in the question's options.
Step-by-step explanation:
The student has asked to find (gf)(x), where f(x) = 3x and g(x) = 2x. The notation (gf)(x) signifies the composition of functions g and f, meaning we first apply f to x, and then apply g to the result of f(x). We begin by finding f(x), which is 3x, and then substitute this into g(x). So, we apply g(f(x)) = g(3x) = 2(3x). This simplifies to 6x, which is not one of the offered options A, B, C, or D. The correct answer is none of the given choices, and the most accurate representation would be 6x, indicating that the question might have an error or a typo in the provided options.