Find the domain of the function. \[ g(x)=\sqrt{3 x+27} \] What is the domain of \( g \) ?

To find the domain of the function \( g(x) = \sqrt{3x + 27} \), we need to ensure that the expression under the square root is non-negative. This means we set up the inequality: \[ 3x + 27 \geq 0 \] Solving for \( x \), we first subtract 27 from both sides: \[ 3x \geq -27 \] Next, we divide by 3: \[ x \geq -9 \] Thus, the domain of \( g \) is all real numbers \( x \) such that \( x \geq -9 \). In interval notation, this can be expressed as: \[ [-9, \infty) \] --- Let’s take a little detour into the world of square roots! Did you know that the discovery of the square root dates back to ancient civilizations? The Babylonians were particularly adept at approximating square roots over 4,000 years ago! They used methods that resemble our modern techniques, showcasing the timeless human penchant for problem-solving. Now, how about putting those square root skills to use in the real world? Square roots are not just for math class; they're used in engineering, physics, and even finance! For example, when calculating the standard deviation in statistics, the square root helps us understand data spread, leading to better decision-making in business and beyond. Keep searching for those real-world applications!