Find the domain of \( \mathrm{f}(\mathrm{x}) \). \[ f(x)=\sqrt{6 x-42} \] Answer Attempt 1 out of 2 Answer Type: Interval

To determine the domain of \( f(x) = \sqrt{6x - 42} \), we need to ensure that the expression inside the square root is non-negative. Thus, we set up the inequality: \[ 6x - 42 \geq 0 \] Solving this gives: \[ 6x \geq 42 \quad \Rightarrow \quad x \geq 7 \] Therefore, the domain of \( f(x) \) in interval notation is: \[ [7, \infty) \] --- The square root function has been around for ages, tracing back to Babylonian mathematics! They used geometric methods for approximating roots long before the advent of decimals or calculators. It’s pretty incredible to think about mathematics evolving through different civilizations. In real-world situations, square roots show up in various fields, like physics, where they are used to determine distances and in statistics for calculating standard deviations. For instance, if you're dealing with the Pythagorean theorem, square roots allow you to find the hypotenuse of right triangles, making them super handy in construction and navigation!