Question

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

Answer 1

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 \( f(x) \) and \( g(x) \).

1. Domain of \( f(x) = 6x^2 - 2x \): This is a polynomial function, which is defined for all real numbers.

2. Domain of \( g(x) = 2x \): This is also a polynomial function, and thus is defined for all real numbers.

Since both functions are defined for all real numbers, the product \( (fg)(x) = f(x)g(x) \) will also be defined for all real numbers.

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

the set of all real numbers.