Find the domain of the function using interval notation. \( f(x)=\frac{9}{\sqrt{x-2}} \)

1. The function is defined as \[ f(x)=\frac{9}{\sqrt{x-2}}. \] 2. The square root \(\sqrt{x-2}\) is only defined when its argument is non-negative, so \[ x-2 \geq 0 \quad \Rightarrow \quad x \geq 2. \] 3. However, since \(\sqrt{x-2}\) is in the denominator, it cannot be equal to zero. Thus, \[ \sqrt{x-2} \neq 0 \quad \Rightarrow \quad x-2 \neq 0 \quad \Rightarrow \quad x \neq 2. \] 4. Combining the conditions, we require \[ x > 2. \] 5. In interval notation, the domain is \[ (2, \infty). \]