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Question
Given that f(x)=6x2−2x
and g(x)=2x
, what is the domain of (fg)(x)
?(1 point)
Responses

the set of all real numbers
the set of all real numbers

the set of all real numbers except x=0
the set of all real numbers except x is equal to 0

the set of all real numbers except x=13
the set of all real numbers except x is equal to 1 third

the set of all real numbers except x=0
and x=13

Answer 1

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.

1. **Domain of \( f(x) \)**: The function \( f(x) = 6x^2 - 2x \) is a polynomial function, which has a domain of all real numbers, \( \mathbb{R} \).

2. **Domain of \( g(x) \)**: The function \( g(x) = 2x \) is also a polynomial function, which has a domain of all real numbers, \( \mathbb{R} \).

3. **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.**