Determine the Domain of the Function: 20/√(4x-2)

To solve the problem of finding the domain of the function $\frac{20}{\sqrt{4x-2}}$, we need to ensure that the expression under the square root is non-negative, and that we do not divide by zero.

**Step 1:** Solve for when the expression inside the square root is non-negative:

$4x - 2 \geq 0$

Add 2 to both sides:

$4x \geq 2$

Divide both sides by 4:

$x \geq 0.5$

**Step 2:** Ensure the denominator is not zero:

$4x - 2 \neq 0$

From $4x - 2 = 0$, we solve:

$4x = 2$

$x = 0.5$

Since at $x = 0.5$, the denominator becomes zero, we exclude this point. Therefore, x > 0.5 .