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Answer :
Final answer:
The composite function of f and g, represented as f∘g(x), is 49x^2 - 343x^3. The domain of this function, using interval notation, is all real numbers, from negative infinity to positive infinity (-∞, ∞).
Explanation:
The question requires us to find the composite function f∘g(x) and its domain for the given functions f(x) = x^2 - x^3 and g(x) = 7x. The composite function f∘g(x) is found by plugging g(x) into f(x), which results in f(g(x)) = (7x)^2 - (7x)^3 = 49x^2 - 343x^3. The second part of the question asks for the domain of this composite function in interval notation. The domain, in this case, is all real numbers since there are no restrictions on x in this polynomial function. Therefore, f∘g(x) = 49x^2 - 343x^3, with the domain being all real numbers in interval notation (-∞, ∞).
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