Find the domain of the function. \( g(x)=\sqrt{5 x+35} \) What is the domain of \( g \) ? (Type your answer in interval notation.)

To determine the domain of the function \( g(x) = \sqrt{5x + 35} \), we need to ensure that the expression inside the square root is non-negative, as the square root of a negative number is not defined in the set of real numbers. 1. **Set the radicand (expression inside the square root) to be non-negative:** \[ 5x + 35 \geq 0 \] 2. **Solve for \( x \):** \[ 5x \geq -35 \] \[ x \geq -7 \] This inequality tells us that \( x \) must be greater than or equal to \(-7\) for \( g(x) \) to be real and defined. **Therefore, the domain of \( g \) in interval notation is:** \[ [-7, \infty) \] **Answer:** \([-7,\,\infty)\)