Final answer:
The product of the functions f(x) and g(x) is (f · g)(x) = 21x^3 - 55x^2. To find (f · g)(3), substitute x with 3 to get 72.
Step-by-step explanation:
The student has asked to find the product of the functions f(x) = 7x - 2 and g(x) = 3x^2 - 7x - 2, denoted as (f · g)(x), as well as the value of this product when x = 3, denoted as (f · g)(3).
To find (f · g)(x), we multiply the functions f(x) and g(x) together:
- f(x) · g(x) = (7x - 2) · (3x^2 - 7x - 2)
- Expand the product: 21x^3 - 49x^2 - 14x - 6x^2 + 14x + 4
- Combine like terms: 21x^3 - 55x^2
Now, to find (f · g)(3), we substitute x with 3:
- (f · g)(3) = 21(3)^3 - 55(3)^2
- Calculate the powers: 21(27) - 55(9)
- Perform the multiplication: 567 - 495
- Subtract to find the result: 72
Therefore, (f · g)(x) = 21x^3 - 55x^2, and (f · g)(3) = 72.