Find the domain of the function. \( f(x)=\sqrt{x-9} \) The domain of \( f(x) \) is \( \square \). (Type your answer in interval notation.)

To find the domain of the function \( f(x) = \sqrt{x-9} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative. This means that \( x - 9 \geq 0 \). Solving for \( x \), we find that \( x \geq 9 \). Therefore, the domain of \( f(x) \) in interval notation is \([9, \infty)\). By understanding functions like this, you can see how they relate to real-life situations, such as determining when the output of a situation (like a distance) can actually exist. For example, you can’t take the square root of a negative quantity when calculating length or height, which means knowing the domain is crucial! To tackle similar problems, remember to always consider any constraints on the variable within the function. A common mistake is to isolate terms without evaluating conditions like square roots and logarithms, which can lead to incorrect conclusions about the domain. Make sure to check these limits carefully!