Determining the Domain: Rational Function with a Square Root Denominator

To solve this problem, we need to determine where the function $f(x) = \frac{2x+2}{\sqrt{2x-8}}$ is defined.

For the fraction to be defined, the denominator cannot be zero, and for the square root to be defined, the radicand (the expression inside the square root) must be non-negative.

Therefore, we need to solve the inequality:

$2x - 8 \geq 0$

Solving this inequality involves the following steps:

• Add 8 to both sides: $2x \geq 8$
• Divide both sides by 2: $x \geq 4$

However, if $x = 4$, the expression inside the square root is zero, making the denominator zero and the overall expression undefined.

As a result, the domain of the function is $x > 4$.

Therefore, the domain of the function is $x > 4$.