Math

QuestionComplete the table using the function f(x)=x4f(x)=\sqrt{x-4}. Simplify answers or mark as "Not a real number" if needed.

Studdy Solution

STEP 1

Assumptions1. The function rule is f(x)=x4f(x)=\sqrt{x-4} . The values of xx are0,4,13, and853. We need to find the corresponding f(x)f(x) values for each xx value4. If the value inside the square root is negative, the result is not a real number

STEP 2

First, let's find the value of f(x)f(x) when x=0x=0. We can do this by substituting x=0x=0 into the function rule.
f(0)=04f(0)=\sqrt{0-4}

STEP 3

implify the expression inside the square root.
f(0)=f(0)=\sqrt{-}

STEP 4

Since the value inside the square root is negative, the result is not a real number. So, f(0)f(0) is not a real number.

STEP 5

Next, let's find the value of f(x)f(x) when x=4x=4. We can do this by substituting x=4x=4 into the function rule.
f(4)=44f(4)=\sqrt{4-4}

STEP 6

implify the expression inside the square root.
f(4)=0f(4)=\sqrt{0}

STEP 7

The square root of0 is0. So, f(4)=0f(4)=0.

STEP 8

Next, let's find the value of f(x)f(x) when x=13x=13. We can do this by substituting x=13x=13 into the function rule.
f(13)=134f(13)=\sqrt{13-4}

STEP 9

implify the expression inside the square root.
f(13)=9f(13)=\sqrt{9}

STEP 10

The square root of9 is3. So, f(13)=3f(13)=3.

STEP 11

Finally, let's find the value of f(x)f(x) when x=85x=85. We can do this by substituting x=85x=85 into the function rule.
f(85)=854f(85)=\sqrt{85-4}

STEP 12

implify the expression inside the square root.
f(85)=81f(85)=\sqrt{81}

STEP 13

The square root of81 is9. So, f(85)=9f(85)=9.
The completed table is\begin{tabular}{|c|c|} \hlinexx & f(x)f(x) \\ \hline0 & Not a real number \\ \hline &0 \\ \hline13 &3 \\ \hline85 &9 \\ \hline\end{tabular}

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