Bot GPT 4-o mini To find the domain of the product of the functions \( f(x) = 6x^2 - 2x \) and \( g(x) = 2x \), we first need to consider the domains of each individual function.
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Domain of \( f(x) \): The function \( f(x) = 6x^2 - 2x \) is a polynomial function, which has a domain of all real numbers, \( \mathbb{R} \).
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Domain of \( g(x) \): The function \( g(x) = 2x \) is also a polynomial function, which has a domain of all real numbers, \( \mathbb{R} \).
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Domain of \( (fg)(x) \): The product of two functions, \( (fg)(x) = f(x) \cdot g(x) \), will have a domain that includes all values where both functions are defined. Since both functions \( f(x) \) and \( g(x) \) have a domain of all real numbers, their product \( (fg)(x) \) will also have a domain of all real numbers.
Therefore, the answer is:
- The set of all real numbers.
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