Find the domain of the following function. \( g(x)=\frac{1}{\sqrt{13+x}} \) The domain is \( \square \). (Type your answer in interval notation.)

To determine the domain of the function \( g(x) = \frac{1}{\sqrt{13 + x}} \), we need to ensure that the expression inside the square root is positive and not zero (since it's in the denominator). 1. **Square Root Condition:** \[ 13 + x > 0 \implies x > -13 \] This ensures that the square root is defined and positive. 2. **Denominator Condition:** \[ \sqrt{13 + x} \neq 0 \implies 13 + x \neq 0 \implies x \neq -13 \] This prevents division by zero. Combining both conditions, the domain of \( g(x) \) is all real numbers greater than \(-13\). **Domain:** \( (-13, \infty) \) **Answer:** \((-13, \infty)\)