Uncover the Domain of a Radical Rational Function: (x+7)/√(x-7)

To determine the domain of the function $\frac{x+7}{\sqrt{x-7}}$, we need to ensure the denominator remains defined and non-zero. As follows:

First, focus on the denominator $\sqrt{x-7}$. The expression under the square root, $x-7$, must be greater than zero for the square root to be defined and not produce zero in the denominator:

• $x - 7 > 0$

This simplifies to:

• $x > 7$

Since the expression under the square root must always be positive for this rational function to be defined, and $\sqrt{x-7}$ in the denominator implies it cannot equal zero, our analysis is complete. Consequently, the domain of the function is the set of all $x$ such that:

The domain of the function is $x > 7$.