Find the domain of the function. \( g(x)=\frac{\sqrt{x-2}}{x-5} \) What is the domain of \( g \) ? (Type your answer in interval notation.)

To find the domain of the function \( g(x) = \frac{\sqrt{x-2}}{x-5} \), we need to consider the following conditions: 1. **Square Root Condition**: - The expression inside the square root must be non-negative: \[ x - 2 \geq 0 \implies x \geq 2 \] 2. **Denominator Condition**: - The denominator cannot be zero: \[ x - 5 \neq 0 \implies x \neq 5 \] Combining these two conditions, the domain of \( g(x) \) consists of all real numbers \( x \) such that \( x \geq 2 \) but \( x \) is not equal to 5. In interval notation, this is expressed as: \[ [2, 5) \cup (5, \infty) \] **Answer:** \([2,5) \cup (5,\infty)\)