Find the Domain of 5/√(x-5): Analyzing Function Restrictions

To determine the domain of the function $\frac{5}{\sqrt{x-5}}$, we must ensure that the expression inside the square root, $x-5$, is positive. Furthermore, because the square root is in the denominator, $x-5$ must be greater than zero:

• Step 1: Set the argument of the square root greater than zero: $x-5 > 0$.
• Step 2: Solve the inequality: Add 5 to both sides to get $x > 5$.

Since the inequality $x > 5$ ensures that the denominator is neither zero nor negative, it defines the domain of the function. Thus, the function $\frac{5}{\sqrt{x-5}}$ is defined for all real numbers $x$ where $x > 5$.

Therefore, the domain of the function is $x > 5$.