Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$. Find the domain of the function.
$$( f \cdot g ) ( x )$$
A) $\quad ( - \infty , \infty )$
B) $\quad ( - \infty , 0 ]$
C) $( - \infty , 0 )$
D) $[ 0 , \infty )$
E) $\quad ( 0 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the function is the set of all possible values of $x$ for which $f \cdot g$ is defined.

We have:

$$(f \cdot g)(x) = f(x) \cdot g(x) = (2x-1)(3x-2) = 6x^2-10x-3$$

This is a polynomial function, which is defined for all real values of $x$. Therefore, the domain of the function is $(-\infty,\infty)$.

Thus, the answer is $\boxed{	ext{(A)}}$.

Let f(x)=2x−1,g(x)=3x−2f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2f(x)=2x−1,g(x)=3x−2

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$