Find the domain of the function $f(x) = \frac{x-3}{\sqrt{x-5}}$.

1. Problem Description

Find the domain of the function $f(x) = \frac{x-3}{\sqrt{x-5}}$.

2. Solution Steps

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, we need to consider two restrictions:

First, since we have a square root in the denominator, the expression inside the square root must be greater than or equal to

0. $x - 5 \ge 0$

Second, since the square root is in the denominator, the entire denominator cannot be equal to

0. Therefore, the expression inside the square root must be strictly greater than

0. $x - 5 > 0$

$x > 5$

This means that $x$ must be greater than

5. In interval notation, this is $(5, \infty)$.

3. Final Answer

(A) $(5, \infty)$