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

Question

Quizplus · Accepted Answer

To find the domain of $( f \cdot g ) ( x )$, we need to find the values of $x$ for which the multiplication of $f(x)$ and $g(x)$ is defined.

$( f \cdot g ) ( x )$ is given by:
$$( f \cdot g ) ( x ) = f(x) \cdot g(x) = (2x - 1) \cdot (3x - 2)$$

For the multiplication to be defined, both the factors on the right-hand side must be defined.

The domain of $f(x)$ is all real numbers (since it is a linear function). 
The domain of $g(x)$ is also all real numbers (since it is a linear function).

Therefore, the domain of $( f \cdot g ) ( x )$ is all real numbers, which is represented as $( -\infty, \infty )$.

Hence, the correct answer is D.

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