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------------------------------------------------ Use the function [tex]f(x) = -8x + 2[/tex] to answer the following questions:

1. Evaluate [tex]f(-1)[/tex]:

[tex]
f(-1) = 10
[/tex]

2. For what value(s) of [tex]x[/tex] does [tex]f(x) = 66[/tex]?

[tex]
x =
[/tex]

Let's solve the problem step-by-step:

1. Evaluate [tex]$ f(-1) $[/tex]:

We are given the function [tex]$ f(x) = -8x + 2 $[/tex].

To find [tex]$ f(-1) $[/tex], substitute [tex]$-1$[/tex] for [tex]$ x $[/tex] in the function:

[tex]\[
f(-1) = -8(-1) + 2
\][/tex]

[tex]\[
f(-1) = 8 + 2
\][/tex]

[tex]\[
f(-1) = 10
\][/tex]

2. Find the value(s) of [tex]$ x $[/tex] for which [tex]$ f(x) = 66 $[/tex]:

We need to solve for [tex]$ x $[/tex] when [tex]$ f(x) = 66 $[/tex].

Set the function equal to 66:

[tex]\[
-8x + 2 = 66
\][/tex]

First, subtract 2 from both sides:

[tex]\[
-8x = 64
\][/tex]

Now, divide both sides by [tex]$-8$[/tex]:

[tex]\[
x = -8
\][/tex]

So, the solution to the problem is:
- [tex]$ f(-1) = 10 $[/tex]
- The value of [tex]$ x $[/tex] for which [tex]$ f(x) = 66 $[/tex] is [tex]$ x = -8 $[/tex].