To solve this problem, we need to understand the process of evaluating the function [tex]\( f(x) \)[/tex] at [tex]\( x + 6 \)[/tex]. The given function is:
[tex]\[ f(x) = x^2 - 5x + 4 \][/tex]
Now, we want to find the value of [tex]\( f(x + 6) \)[/tex].
### Step-by-Step Solution:
1. Identify the Function [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x^2 - 5x + 4 \][/tex]
2. Substitute [tex]\( x + 6 \)[/tex] into the Function:
To find [tex]\( f(x + 6) \)[/tex], we replace each occurrence of [tex]\( x \)[/tex] in the function with [tex]\( x + 6 \)[/tex].
3. Replace [tex]\( x \)[/tex] in the Function:
- Original function: [tex]\( f(x) \)[/tex]
- To evaluate [tex]\( f(x + 6) \)[/tex], replace each [tex]\( x \)[/tex] with [tex]\( x + 6 \)[/tex]
Thus, each occurrence of [tex]\( x \)[/tex] in the function should be replaced with [tex]\( x + 6 \)[/tex].
### Filling the Blanks:
Given the function [tex]\( f(x) = x^2 - 5x + 4 \)[/tex], if we want to find [tex]\( f(x + 6) \)[/tex], we replace each occurrence of [tex]\( x \)[/tex] by [tex]\( x + 6 \)[/tex].
Therefore, the filled statement should look like this:
If [tex]\( f(x) = x^2 - 5x + 4 \)[/tex], it is possible to find [tex]\( f(x + 6) \)[/tex] by replacing each occurrence of [tex]\( x \)[/tex] by [tex]\( x + 6 \)[/tex].
