College Algebra
Homework: Homework 1A
Question 6

Fill in each blank so that the resulting statement is true.

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].



Answer :

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].