Final answer:
To evaluate (f * g)(3), calculate f(3) as 9 and g(3) as 6; then multiply both to get 54. The correct answer is D. 54.
Step-by-step explanation:
The student is asking to evaluate the function (f * g)(3), which means we need to multiply the results of two functions, f(x) and g(x), when x is equal to 3.
The function f(x) = 4x - 3 and g(x) = x^2 + x - 6. First, we will evaluate both functions separately at x = 3.
For f(3), we substitute 3 into the function f(x):
f(3) = 4(3) - 3 = 12 - 3 = 9.
Next, we substitute 3 into the function g(x):
g(3) = 3^2 + 3 - 6 = 9 + 3 - 6 = 6.
Now, multiply the results of f(3) and g(3) to evaluate (f * g)(3):
(f * g)(3) = f(3) * g(3) = 9 * 6 = 54.
Therefore, the answer is D. 54.