Find the domain of the function \( f(x)=\sqrt{2 x+6} \) a) \( [-3, \infty) \) b) \( [3, \infty) \) c) \( (-3, \infty) \) d) \( (-\infty, 3] \) e) \( (-\infty,-3] \)

To find the domain of the function \( f(x) = \sqrt{2x + 6} \), we need to ensure that the expression inside the square root is non-negative. This means we must solve the inequality: \[ 2x + 6 \geq 0 \] Subtracting 6 from both sides gives us: \[ 2x \geq -6 \] Dividing by 2 results in: \[ x \geq -3 \] Therefore, the domain of the function is \( [-3, \infty) \). So the correct option is: **a) \( [-3, \infty) \)** --- Here's some additional information to keep the math vibes flowing! Did you know that square roots have historical roots in mathematics dating back to ancient civilizations? The Babylonians were among the earliest to develop methods for calculating square roots, using iterative guesswork that is quite similar to the methods we still use today! If you're ever puzzled by domains, remember to always check for values that cause functions to go "divide by zero," or negative numbers under roots. Missing these can lead you to mistakenly include numbers in your domain that simply don't work, so keep an eye out for those pesky errors!