Questions: Fill in the table using this function rule. f(x) = √(x-3) Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) 3 0 52 7 84 9 103

Fill in the table using this function rule.
f(x) = √(x-3)

Simplify your answers as much as possible.
Click "Not a real number" if applicable.

x f(x)
3 0
52 7
84 9
103

Transcript text: Fill in the table using this function rule. \[ f(x)=\sqrt{x-3} \] Simplify your answers as much as possible. Click "Not a real number" if applicable. \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline 3 & 0 \\ \hline 52 & 7 \\ \hline 84 & 9 \\ \hline 103 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Understand the function

The given function is $ f(x) = \sqrt{x - 3} $. This is a square root function, and its domain is all real numbers $ x $ such that $ x - 3 \geq 0 $, or $ x \geq 3 $. For values of $ x $ less than 3, the function is not a real number.

Step 2: Evaluate $ f(x) $ for $ x = 103 $

We are asked to find $ f(103) $. Substitute $ x = 103 $ into the function: \[ f(103) = \sqrt{103 - 3} = \sqrt{100}. \] The square root of 100 is 10.

Step 3: Simplify the result

The value of $ f(103) $ simplifies to 10. Since 100 is a perfect square, the result is an integer.