Find the domain of the function. \( g(x)=\frac{x+7}{x^{2}-16} \) The domain is \( \square \). (Type your answer in interval notation.)

To determine the **domain** of the function \( g(x) = \frac{x+7}{x^{2}-16} \), we need to identify all real numbers \( x \) for which the function is defined. The function \( g(x) \) is a **rational function**, which means it is defined for all real numbers **except** those that make the **denominator** equal to zero (since division by zero is undefined). 1. **Set the denominator equal to zero and solve for \( x \):** \[ x^{2} - 16 = 0 \] \[ x^{2} = 16 \] \[ x = \pm 4 \] 2. **Exclude these values from the domain:** The function is undefined at \( x = 4 \) and \( x = -4 \). 3. **Express the domain in interval notation:** \[ (-\infty, -4) \cup (-4, 4) \cup (4, \infty) \] **Final Answer:** The domain is \( (-\infty, -4) \cup (-4, 4) \cup (4, \infty) \).