To solve the problem, we need to find [tex]\( f(x-3) \)[/tex] for the given function [tex]\( f(x) = 6x + 2 \)[/tex].
Let's break it down step by step:
1. Substitute [tex]\( x - 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
The function [tex]\( f(x) \)[/tex] is given as:
[tex]\[
f(x) = 6x + 2
\][/tex]
To find [tex]\( f(x-3) \)[/tex], substitute [tex]\( x-3 \)[/tex] in place of [tex]\( x \)[/tex] in the given function:
[tex]\[
f(x-3) = 6(x-3) + 2
\][/tex]
2. Distribute and simplify:
Now, distribute the 6 in the expression [tex]\( 6(x-3) \)[/tex]:
[tex]\[
f(x-3) = 6(x) - 6(3) + 2
\][/tex]
Simplify the terms inside the parentheses:
[tex]\[
f(x-3) = 6x - 18 + 2
\][/tex]
Combine the constant terms:
[tex]\[
f(x-3) = 6x - 16
\][/tex]
Therefore, the simplified expression for [tex]\( f(x-3) \)[/tex] is:
[tex]\[
f(x-3) = 6x - 16
\][/tex]
The correct answer is:
[tex]\[
f(x-3) = 6x - 16
\][/tex]
