Final answer:
The composite function f(g(x)) with f(x) = 2x³ and g(x) = 3x² results in f(g(x)) = 2(3x²)³ = 54x⁶, which does not match any of the provided answer options.
Step-by-step explanation:
When calculating the composite function f(g(x)), you substitute the g function into the f function. The composite function f(g(x)) with f(x) = 2x³ and g(x) = 3x² results in f(g(x)) = 2(3x²)³ = 54x⁶, which does not match any of the provided answer options. In this case, we have f(x) = 2x³ and g(x) = 3x². To find f(g(x)), replace every x in f(x) with g(x).
f(g(x)) = f(3x²) = 2(3x²)³. Now, we calculate the cube of the entire expression inside the parentheses, which means we cube both the digit and the variable part. (3x²)³ becomes 3³ * x²³ = 27x⁶, after cubing the coefficient and multiplying the exponents. Multiplied with 2, we get 54x⁶, which is not one of the answer options provided, indicating a possible error in the options.