Find the domain of \( f(x)=-\sqrt{6 x-24} \). The domain is \( x \geq \) The solution is

To find the domain of \( f(x) = -\sqrt{6x - 24} \), we need to ensure that the expression inside the square root is non-negative. This requires solving the inequality: \[ 6x - 24 \geq 0. \] By adding 24 to both sides, we get: \[ 6x \geq 24. \] Next, divide by 6: \[ x \geq 4. \] Thus, the domain of the function is \( x \geq 4 \). Remember that since we're dealing with the square root, any values below this threshold would yield a negative number under the square root, which isn't permissible in the realm of real numbers. Get your graphing tools ready; the function will only be defined out in the beautiful landscape starting from 4 and heading to infinity. Notably, understanding the behavior of functions and their graphs helps visualize where they are defined. Consider plotting it on a graph; you’ll see that the curve will extend infinitely rightward, starting at the point (4, 0).