Find the domain of the function. $$ f(x)=\frac{9 x}{\sqrt{x-2}} $$ The domain is

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To determine the domain of the function $$ f(x) = \frac{9x}{\sqrt{x-2}} $$, we need to identify all real numbers $$ x $$ for which the function is defined.

1. **Square Root Constraint**:
   - The expression inside the square root, $$ x - 2 $$, must be non-negative to ensure the square root is real.
   $$
   x - 2 \geq 0 \implies x \geq 2
   $$

2. **Denominator Constraint**:
   - The denominator $$ \sqrt{x-2} $$ cannot be zero, as division by zero is undefined.
   $$
   \sqrt{x-2} \neq 0 \implies x - 2 \neq 0 \implies x \neq 2
   $$

Combining these two constraints:
- $$ x \geq 2 $$ from the square root condition.
- $$ x \neq 2 $$ from the denominator condition.

Therefore, the domain of $$ f(x) $$ is all real numbers **greater than** 2.

**Domain:** $$ (2,\ \infty) $$
The domain of the function $$ f(x) = \frac{9x}{\sqrt{x-2}} $$ is all real numbers greater than 2, which is $$ (2, \infty) $$.

Find the domain of the function.

The domain is

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Find the domain of the function. The domain is