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Answer :
Final answer:
To find f ∘ (f ⋅ g)(6), calculate f ⋅ g and substitute the value of 6 into the resulting function to get 918.
Explanation:
We are given f(x) = x(x - 1) and g(x) = 3x. To find f ∘ (f ⋅ g)(6), we need to first calculate f ⋅ g and then substitute the value of 6 into the resulting function.
f ⋅ g(x) = f(g(x)) = f(3x) = (3x)((3x) - 1) = 9x(3x - 1) = 27x² - 9x.
Now, we can substitute 6 into f ⋅ g(x) to find the final result. f ∘ (f ⋅ g)(6) = 27(6)² - 9(6) = 27(36) - 54 = 972 - 54 = 918. Therefore, the correct answer is 918.
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