Given that f(x)=6x2−2x

Question

and g(x)=2x
, what is the domain of (fg)(x)
?(1 point)
Responses

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
the set of all real numbers

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=13

Answer 1

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

Given:

• \( f(x) = 6x^2 - 2x \) is a polynomial function, and the domain of a polynomial function is all real numbers.
• \( g(x) = 2x \) is also a polynomial function, which also has a domain of all real numbers.

Since both functions are defined for all real numbers, their product \( (fg)(x) \) is also defined for all real numbers.

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

the set of all real numbers.