Find the Domain of 3/√(2x-3): Square Root Function Analysis

To solve this problem, we need to determine the domain of the function given by $\frac{3}{\sqrt{2x-3}}$. The fraction is undefined whenever the denominator is zero, and the square root requires the expression inside to be positive.

Let's break down the steps:

• Since the square root is in the denominator, $2x - 3$ must be strictly greater than zero.
• Set up the inequality: $2x - 3 > 0$.
• Solve the inequality for $x$:
• Add 3 to both sides: $2x > 3$.
• Divide both sides by 2: $x > 1.5$.

The domain of the function is all real numbers $x$ such that $x > 1.5$. Therefore, we write the domain as $x > 1.5$.

Hence, the correct choice among the given options is: $x > 1.5$ which corresponds to choice number 3.