Analyzing the Domain of 3/√(x-10): Understanding Function Constraints

To find the domain of the function $f(x) = \frac{3}{\sqrt{x-10}}$, follow these steps:

• First, ensure the expression under the square root, $x-10$, is non-negative. This gives $x-10 \geq 0$, or equivalently, $x \geq 10$.
• Second, the denominator of the function, $\sqrt{x-10}$, cannot be zero. This means $\sqrt{x-10} \neq 0$, leading to $x-10 \neq 0$. Therefore, $x \neq 10$.

Combining these conditions, the value of $x$ must satisfy $x > 10$. This ensures both the definition of the square root and the non-zero nature of the denominator.

The correct domain of the function is $x > 10$.