Question

Given that f(x)=6x^2 −2x and g(x)=2x , what is the domain of (fg)(x) ?(1 point) Responses 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 except x=13 the set of all real numbers except x is equal to 1 third the set of all real numbers

Answer 1

To find the domain of the product function \((fg)(x) = f(x) \cdot g(x)\), we first need to determine the individual domains of \(f(x)\) and \(g(x)\).

Given:

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

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

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

The set of all real numbers.