Find the domain of the function. $$ g(x)=\frac{1}{5-3 x} $$ Choose the correct domain below. A. $$ \{x \mid x $$ is a real number and $$ x
eq 1\} $$ B. $$ \{x \mid x $$ is a real number and $$ x
eq 0\} $$ C. $$ \left\{x \mid x ight. $$ is a real number and $$ \left.x
eq \frac{5}{3} ight\} $$ O D. $$ \left\{x \mid x ight. $$ is a real number and $$ \left.x \geq \frac{5}{3} ight\} $$

Question

Find the domain of the function. $$ g(x)=\frac{1}{5-3 x} $$ Choose the correct domain below. A. $$ \{x \mid x $$ is a real number and $$ x 
eq 1\} $$ B. $$ \{x \mid x $$ is a real number and $$ x 
eq 0\} $$ C. $$ \left\{x \mid xight. $$ is a real number and $$ \left.x 
eq \frac{5}{3}ight\} $$ O D. $$ \left\{x \mid xight. $$ is a real number and $$ \left.x \geq \frac{5}{3}ight\} $$

UpStudy AI · Accepted Answer

To determine the domain of the function $$ g(x) = \frac{1}{5 - 3x} $$, we need to identify all real numbers $$ x $$ for which the function is defined. The function will be undefined when the denominator equals zero because division by zero is not allowed.

**Step 1: Set the denominator equal to zero and solve for $$ x $$.**

$$
5 - 3x = 0
$$
$$
3x = 5
$$
$$
x = \frac{5}{3}
$$

**Step 2: Exclude this value from the domain.**

Therefore, the function $$ g(x) $$ is defined for all real numbers except $$ x = \frac{5}{3} $$.

**Conclusion:**

The correct domain is:
$$
\left\{x \mid x \text{ is a real number and } x \neq \frac{5}{3}\right\}
$$

**Answer:**  
C. $$ \left\{x \mid x\right. $$ is a real number and $$ \left.x \neq \frac{5}{3}\right\} $$
The domain of $$ g(x) = \frac{1}{5 - 3x} $$ is all real numbers except $$ x = \frac{5}{3} $$. **Answer:** C. $$ \left\{x \mid x\right. $$ is a real number and $$ \left.x \neq \frac{5}{3}\right\} $$

Find the domain of the function.

Choose the correct domain below.
A. is a real number and
B. is a real number and
C. is a real number and
O D. is a real number and

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