Determine the Domain: Analyzing the Function 4x-10 over √(2.5x-10)

Look at the following function:

$\frac{4x-10}{\sqrt{2.5x-10}}$

What is the domain of the function?

To find the domain of the function $\frac{4x-10}{\sqrt{2.5x-10}}$, we need to ensure the expression under the square root is positive since it cannot equal zero or be negative.

Step 1: Set up the inequality based on the square root:

$2.5x - 10 > 0$

Step 2: Solve the inequality for $x$:

• Add 10 to both sides: $2.5x > 10$
• Divide both sides by 2.5: $x > \frac{10}{2.5}$
• Calculate: $x > 4$

Step 3: Interpret the result:

The domain of the function is all real numbers greater than 4, $x > 4$, ensuring the expression inside the square root is always positive.

Thus, the correct domain is represented by choice 2: $x > 4$.