If $f(x)=\frac{\sqrt{x}-7}{6}$, what is the value of $f(3)$, to the nearest thousandth (if necessary)?

Step 1 ：Given the function \(f(x)=\frac{\sqrt{x}-7}{6}\), we are asked to find the value of \(f(3)\).

Step 2 ：To find this, we substitute \(x\) with \(3\) in the function \(f(x)\).

Step 3 ：So, \(f(3) = \frac{\sqrt{3}-7}{6}\).

Step 4 ：After calculating, we find that \(f(3) = -0.8779915320718539\).

Step 5 ：To the nearest thousandth, this is \(-0.878\).

Step 6 ：Final Answer: The value of \(f(3)\), to the nearest thousandth, is \(\boxed{-0.878}\).