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------------------------------------------------ Given the function below, determine the following:

[tex]\[ f(x) = 11x - 9 \][/tex]

1. Find [tex]$ f(5) $[/tex].
[tex]$ f(5) = $[/tex]

2. Find [tex]$ f(-8) $[/tex].

3. Find [tex]$ x $[/tex] if [tex]$ f(x) = 57 $[/tex].

Sure! Let's go step by step to solve each part of the problem using the function [tex]$ f(x) = 11x - 9 $[/tex].

1. Find [tex]$ f(5) $[/tex]:
- To find [tex]$ f(5) $[/tex], substitute [tex]$ x = 5 $[/tex] into the function.
- Calculate: [tex]$ f(5) = 11 \times 5 - 9 $[/tex].
- Simplifying: [tex]$ f(5) = 55 - 9 = 46 $[/tex].
- So, [tex]$ f(5) = 46 $[/tex].

2. Find [tex]$ f(-8) $[/tex]:
- To find [tex]$ f(-8) $[/tex], substitute [tex]$ x = -8 $[/tex] into the function.
- Calculate: [tex]$ f(-8) = 11 \times (-8) - 9 $[/tex].
- Simplifying: [tex]$ f(-8) = -88 - 9 = -97 $[/tex].
- So, [tex]$ f(-8) = -97 $[/tex].

3. Find [tex]$ x $[/tex] if [tex]$ f(x) = 57 $[/tex]:
- Set the function equal to 57: [tex]$ 11x - 9 = 57 $[/tex].
- First, add 9 to both sides to isolate the term with [tex]$ x $[/tex]: [tex]$ 11x = 57 + 9 $[/tex].
- Simplify the equation: [tex]$ 11x = 66 $[/tex].
- Divide both sides by 11 to solve for [tex]$ x $[/tex]: [tex]$ x = \frac{66}{11} = 6 $[/tex].
- So, [tex]$ x = 6 $[/tex] when [tex]$ f(x) = 57 $[/tex].

I hope this step-by-step solution helps you understand the process! Let me know if you have any more questions.