Find the Domain of 12/√(4x-4): Square Root Function Analysis

To find the domain of the function $\frac{12}{\sqrt{4x-4}}$, let's analyze the conditions necessary for the function to be defined.

The expression under the square root, $4x - 4$, must be positive, as the square root of a negative number is not defined in the real numbers, and division by zero is undefined. Therefore, we need:

• $4x - 4 > 0$

Solve this inequality step by step:

• Add 4 to both sides: $4x - 4 + 4 > 0 + 4$, which simplifies to $4x > 4$.
• Divide both sides by 4: $\frac{4x}{4} > \frac{4}{4}$, which simplifies to $x > 1$.

The inequality $x > 1$ describes the domain of the function.

Therefore, the domain of the function $\frac{12}{\sqrt{4x-4}}$ is $x > 1$.