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

To determine the domain of the function $\frac{3}{\sqrt{x-2}}$, we need to consider the constraints imposed by the square root and the fraction.

First, the expression inside the square root must be non-negative: $x - 2 \geq 0$. This simplifies to:

• $x \geq 2$

However, because the expression $\sqrt{x-2}$ is in the denominator of the fraction, we must also ensure that it is not equal to zero, as division by zero is undefined. Therefore, we have:

• $x - 2 \neq 0$

Solving this inequality gives:

• $x \neq 2$

Together, the solution to both conditions is that $x$ must be greater than 2 to ensure the function is defined. Thus, the domain of the function is:

$x > 2$

Therefore, the correct choice for the domain is $x > 2$.