Final answer:
The correct answer is B, which represents the composite function (f ∗ g)(x) found by substituting g(x) into f(x) resulting in the expression 3x^2 - 17.
Step-by-step explanation:
To find (x), we substitute the given expressions for f(x) and g(x) into the options and see which one matches the given equation.
Substituting f(x) = 3x + 1 and g(x) = x^2 - 6 into option B gives us (3x + 1)(x^2 - 6).
Therefore, the correct answer is option B: 3x + 1(x^2 - 6).
The correct answer is option B. To find the composite function (f ∗ g)(x), also written as f(g(x)), you first apply the function g to x and then apply the function f to the result of g(x). So, for the given functions f(x) = 3x + 1 and g(x) = x2 - 6, we proceed as follows:
- First, we calculate g(x) = x2 - 6.
- Then, we substitute this result into the function f. So instead of x in f(x), we insert g(x) = x2 - 6 yielding f(g(x)) = 3(x2 - 6) + 1.
- Simplifying gives us f(g(x)) = 3x2 - 18 + 1, which simplifies further to 3x2 - 17.
The composed function f(g(x)) or (f ∗ g)(x) is thus represented by the algebraic expression 3x2 - 17, matching option B.