Questions: Fill in the table using this function rule. f(x) = sqrt(9-x) Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) -40 9 18 20

Solution Steps

To solve this problem, we need to evaluate the function \( f(x) = \sqrt{9-x} \) for each given value of \( x \). If the expression under the square root is negative, the result is not a real number. We will check each \( x \) value, compute \( f(x) \), and determine if the result is a real number or not.

We calculate \( f(-40) \) using the function \( f(x) = \sqrt{9 - x} \): \[ f(-40) = \sqrt{9 - (-40)} = \sqrt{9 + 40} = \sqrt{49} = 7.0 \]

Next, we evaluate \( f(9) \): \[ f(9) = \sqrt{9 - 9} = \sqrt{0} = 0.0 \]

Now, we evaluate \( f(18) \): \[ f(18) = \sqrt{9 - 18} = \sqrt{-9} \] Since the square root of a negative number is not a real number, we conclude: \[ f(18) = \text{Not a real number} \]

Finally, we evaluate \( f(20) \): \[ f(20) = \sqrt{9 - 20} = \sqrt{-11} \] Again, since the square root of a negative number is not a real number, we conclude: \[ f(20) = \text{Not a real number} \]

Final Answer