High School

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Use the following function rule to find [tex]f(-100)[/tex].

[tex]
\begin{array}{l}
f(x) = -\sqrt{-84 - x} \\
f(-100) = \square
\end{array}
[/tex]

Answer :

We are given the function

[tex]$$
f(x) = -\sqrt{-84 - x}.
$$[/tex]

To find [tex]$f(-100)$[/tex], we follow these steps:

1. Substitute [tex]$x = -100$[/tex] into the function:

[tex]$$
f(-100) = -\sqrt{-84 - (-100)}.
$$[/tex]

2. Simplify the expression under the square root. Notice that subtracting a negative number is equivalent to adding:

[tex]$$
-84 - (-100) = -84 + 100 = 16.
$$[/tex]

3. Now, take the square root of [tex]$16$[/tex]:

[tex]$$
\sqrt{16} = 4.
$$[/tex]

4. Finally, apply the negative sign in front of the square root:

[tex]$$
f(-100) = -4.
$$[/tex]

Thus, the answer is

[tex]$$
f(-100) = -4.
$$[/tex]

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