If $f(x)=\frac{\sqrt{x}-7}{6}$, what is the value of $f(3)$, to the nearest thousandth (if necessary)?
Final Answer: The value of \(f(3)\), to the nearest thousandth, is \(\boxed{-0.878}\).
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 \(\boxed{-0.878}\).