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=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=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 function \((fg)(x)\), we first need to understand the functions involved:

- \(f(x) = 6x^2 - 2x\)
- \(g(x) = 2x\)

Next, we can compute the product of these functions:

\[
(fg)(x) = f(x) \cdot g(x) = (6x^2 - 2x)(2x)
\]

Now, let's simplify \((fg)(x)\):

\[
(fg)(x) = (6x^2 - 2x)(2x) = 12x^3 - 4x^2
\]

Now we consider the domain.

Both \(f(x)\) and \(g(x)\) are polynomial functions. The domain of polynomial functions is typically all real numbers because polynomials are defined for all values of \(x\).

Thus, the domain of \((fg)(x)\) will also be all real numbers, as there are no restrictions or values of \(x\) that would cause the functions to be undefined.

Therefore, the correct response is:

**the set of all real numbers.**