Step 1 :The function rule is \(f(x)=\sqrt{x}-2\). We will use this rule to find the values of \(f(x)\) for each given \(x\).
Step 2 :When \(x=-4\), we have \(f(-4)=\sqrt{-4}-2\). But the square root of a negative number is not a real number. So, \(f(-4)\) is not a real number.
Step 3 :When \(x=0\), we have \(f(0)=\sqrt{0}-2=0-2=-2\).
Step 4 :When \(x=49\), we have \(f(49)=\sqrt{49}-2=7-2=5\).
Step 5 :When \(x=81\), we have \(f(81)=\sqrt{81}-2=9-2=7\).
Step 6 :So, the completed table is: \begin{tabular}{|c|c|} \hline \(x\) & \(f(x)\) \\ \hline -4 & Not a real number \\ \hline 0 & \(-2\) \\ \hline 49 & \(\boxed{5}\) \\ \hline 81 & \(\boxed{7}\) \\ \hline \end{tabular}