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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.