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 \( x \neq 1\} \) B. \( \{x \mid x \) is a real number and \( x \neq 0\} \) C. \( \left\{x \mid x\right. \) is a real number and \( \left.x \neq \frac{5}{3}\right\} \) O D. \( \left\{x \mid x\right. \) is a real number and \( \left.x \geq \frac{5}{3}\right\} \)

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 \( \left.x \neq \frac{5}{3}\right\} \)