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

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=0
and x=13

1 answer

To find the domain of the product \( (fg)(x) \) where \( f(x) = 6x^2 - 2x \) and \( g(x) = 2x \), we need to consider the domains of both functions.

  1. Domain of \( f(x) \):

    • The function \( f(x) = 6x^2 - 2x \) is a polynomial, and the domain of any polynomial is the set of all real numbers.

  2. Domain of \( g(x) \):

    • The function \( g(x) = 2x \) is also a polynomial, and its domain is also the set of all real numbers.

Since both \( f(x) \) and \( g(x) \) have a domain of all real numbers, the product \( (fg)(x) = f(x)g(x) \) will also be defined for all real numbers.

Thus, the domain of \( (fg)(x) \) is:

The set of all real numbers.