Product of a set function: (f ∘ g)(x) = (3x² + 18x + 27)(x - 6)

To find the product of the functions f(x) = 3x² + 18x + 27 and g(x) = x - 6, we can simply multiply them together:

(f ∘ g)(x) = (3x² + 18x + 27)(x - 6)
= 3x²(x - 6) + 18x(x - 6) + 27(x - 6)
= 3x³ - 18x² + 18x² - 108x + 27x - 162
= 3x³ - 81x - 162

Therefore, the product of the functions f(x) = 3x² + 18x + 27 and g(x) = x - 6 is (f ∘ g)(x) = 3x³ - 81x - 162.

(f ∘ g)(x) = 3x² · (x - 6) + 18x · (x - 6) + 27 · (x - 6)
(f ∘ g)(x) = 3x³ - 18x² + 18x² - 108x + 27x - 162
(f ∘ g)(x) = 3x³ - 81x - 162

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