Problem

Radicals Table for a square root function Fill in the table using this function rule. \[ f(x)=\sqrt{x}-2 \] Simplify your answers as much as possible. Click "Not a real number" if applicable. \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline-4 & $\square$ \\ \hline 0 & $\square$ \\ \hline 49 & $\square$ \\ \hline 81 & $\square$ \\ \hline \end{tabular}

Solution

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}

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Source: https://solvelyapp.com/problems/yY8YETFPsJ/

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