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 find the domain of the function \( g(x)=\frac{1}{5-3 x} \), we need to determine values of \( x \) that do not make the denominator equal to zero. Setting the denominator equal to zero gives: \( 5 - 3x = 0 \) Solving for \( x \): \( 3x = 5 \) \( x = \frac{5}{3} \) This means the function is undefined at \( x = \frac{5}{3} \). Therefore, the correct domain is: C. \( \left\{x \mid x\right. \) is a real number and \( \left.x \neq \frac{5}{3}\right\} \)