Final answer:
To find (f ∘ g)(x), substitute g(x) into f(x) and simplify the expression. The result is (f ∘ g)(x) = 3x² - 22x + 24. The domain of (f ∘ g)(x) is all real numbers.
Step-by-step explanation:
To find (f ∘ g)(x), we need to substitute g(x) into f(x) and simplify the expression.
Substituting g(x) = x - 3 into f(x), we get:
(f ∘ g)(x) = f(g(x)) = f(x - 3)
= 3(x - 3)² - 4(x - 3) - 15
= 3(x² - 6x + 9) - 4x + 12 - 15
= 3x² - 18x + 27 - 4x - 3
= 3x² - 22x + 24
The domain of (f ∘ g)(x) is the same as the domain of g(x), which is all real numbers.