College

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].

Answer :

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.

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