The function is defined for values of where , which means . This simplifies to or . Therefore, the domain of this function includes all real numbers outside the interval .

In real-world applications, functions that involve square roots are often used in physics and engineering problems, such as calculating distances or determining rates. For instance, if an engineer is analyzing a cable’s tension where the tension is modeled by a function similar to , understanding its domain will be critical to ensure the design stays within safe operational limits.