Certainly! Let's find the values of the function [tex]\( f(x) = |x-5| + 1 \)[/tex] for specific [tex]\( x \)[/tex] values step by step. We'll evaluate the function for [tex]\( x = 3 \)[/tex], [tex]\( x = 5 \)[/tex], and [tex]\( x = 8 \)[/tex].
### Step-by-Step Solution:
#### 1. Evaluate [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = |3 - 5| + 1 \][/tex]
Calculate the absolute value:
[tex]\[ |3 - 5| = |-2| = 2 \][/tex]
Add 1 to the result:
[tex]\[ f(3) = 2 + 1 = 3 \][/tex]
So, [tex]\( f(3) = 3 \)[/tex].
#### 2. Evaluate [tex]\( f(x) \)[/tex] when [tex]\( x = 5 \)[/tex]:
[tex]\[ f(5) = |5 - 5| + 1 \][/tex]
Calculate the absolute value:
[tex]\[ |5 - 5| = |0| = 0 \][/tex]
Add 1 to the result:
[tex]\[ f(5) = 0 + 1 = 1 \][/tex]
So, [tex]\( f(5) = 1 \)[/tex].
#### 3. Evaluate [tex]\( f(x) \)[/tex] when [tex]\( x = 8 \)[/tex]:
[tex]\[ f(8) = |8 - 5| + 1 \][/tex]
Calculate the absolute value:
[tex]\[ |8 - 5| = |3| = 3 \][/tex]
Add 1 to the result:
[tex]\[ f(8) = 3 + 1 = 4 \][/tex]
So, [tex]\( f(8) = 4 \)[/tex].
### Summary
We have calculated the values of [tex]\( f(x) \)[/tex] for the given [tex]\( x \)[/tex] values:
- [tex]\( f(3) = 3 \)[/tex]
- [tex]\( f(5) = 1 \)[/tex]
- [tex]\( f(8) = 4 \)[/tex]
Therefore, the results for [tex]\( f(x) \)[/tex] at [tex]\( x = 3, 5, \)[/tex] and [tex]\( 8 \)[/tex] are:
[tex]\[ [3, 1, 4] \][/tex]
