Finding the Domain: Analyze the Function (3x+12)/√(5x-10)

The function given is $\frac{3x+12}{\sqrt{5x-10}}$.

To find the domain, we focus on the expression within the denominator's square root: $\sqrt{5x-10}$.

The expression $5x-10$ must be greater than $0$ for the square root to be defined and the denominator to be non-zero.

Let's solve the inequality:

• Set $5x-10 > 0$.
• Add $10$ to both sides: $5x > 10$.
• Divide both sides by $5$: $x > 2$.

This means the domain of the function is all $x$ such that $x > 2$.

The domain is, therefore, correctly expressed as $x > 2$.