What is the domain of ((f)/(g))(x)? f(x) = 2x g(x) = –5x + 3 Choices: [[All real numbers][All real numbers except 3/5][All real numbers except –3/5][All real numbers except 5/3]]

Identify Formula: Identify the formula for ((f)/(g))(x). ((f)/(g))(x) is the quotient of f(x) and g(x), which means we need to divide f(x) by g(x). ((f)/(g))(x) = f(x) / g(x)Given Functions: We have the functions: f(x) = 2x g(x) = –5x + 3 To find the domain of ((f)/(g))(x), we need to determine the values of x for which g(x) is not equal to zero, since division by zero is undefined.Find Domain: Solve for x when g(x) = 0 to find the excluded value from the domain. g(x) = 0 –5x + 3 = 0 –5x = –3 x = –3 / (–5) x = 3/5Solve for Excluded Value: We found that g(x) = 0 when x = 3/5. This means that x = 3/5 is the value that cannot be included in the domain of ((f)/(g))(x) because it would make the denominator zero.

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What is the domain of $\left(\frac{f}{g}\right)(x)$ ? $\newline$ $f(x) = 2x$ $\newline$ $g(x) = -5x + 3$ $\newline$ Choices: $\newline$ $[\text{A]All real numbers}$ $\newline$ $[\text{B]All real numbers except } \frac{3}{5}$ $\newline$ $[\text{C]All real numbers except } -\frac{3}{5}$ $\newline$ $[\text{D]All real numbers except } \frac{5}{3}$

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Q. What is the domain of

\left(\frac{f}{g}\right)(x)

\newline

f(x) = 2x

\newline

g(x) = -5x + 3

\newline

Choices:

\newline

[\text{A]All real numbers}

\newline

[\text{B]All real numbers except } \frac{3}{5}

\newline

[\text{C]All real numbers except } -\frac{3}{5}

\newline

[\text{D]All real numbers except } \frac{5}{3}

Identify Formula: Identify the formula for $((f)/(g))(x)$ . $((f)/(g))(x)$ is the quotient of $f(x)$ and $g(x)$ , which means we need to divide $f(x)$ by $g(x)$ . $((f)/(g))(x) = f(x) / g(x)$
Given Functions: We have the functions: $\newline$ $f(x) = 2x$ $\newline$ $g(x) = -5x + 3$ $\newline$ To find the domain of $\left(\frac{f}{g}\right)(x)$ , we need to determine the values of $x$ for which $g(x)$ is not equal to $0$ , since division by zero is undefined.
Find Domain: Solve for $x$ when $g(x) = 0$ to find the excluded value from the domain. $\newline$ $g(x) = 0$ $\newline$ $–5x + 3 = 0$ $\newline$ $–5x = –3$ $\newline$ $x = –3 / (–5)$ $\newline$ $x = \frac{3}{5}$
Solve for Excluded Value: We found that $g(x) = 0$ when $x = \frac{3}{5}$ . This means that $x = \frac{3}{5}$ is the value that cannot be included in the domain of $\left(\frac{f}{g}\right)(x)$ because it would make the denominator zero.