Examine the Domain of (2x+20)/√(2x-10)

To determine the domain of the function $\frac{2x+20}{\sqrt{2x-10}}$, we must ensure that the expression under the square root is non-negative, because the square root of a negative number is not defined in the real numbers.

We start by analyzing the denominator, specifically the square root, $\sqrt{2x-10}$. For the square root to be valid (for real numbers), we require:

• $2x-10 \geq 0$

Now, solve the inequality $2x - 10 \geq 0$:

• Add 10 to both sides: $2x \geq 10$
• Divide both sides by 2: $x \geq 5$

However, since the expression $2x-10$ also prohibits zero in the denominator (as the square root in the denominator cannot be zero), we strictly have:

• $x > 5$

Thus, the domain of the function is all $x$ such that $x > 5$.

Therefore, the domain of the function $\frac{2x+20}{\sqrt{2x-10}}$ is $x > 5$.