To find [tex]\( f(x-3) \)[/tex] for the given function [tex]\( f(x) = 6x + 2 \)[/tex], follow these steps:
1. Substitute [tex]\( x-3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
The function [tex]\( f(x) \)[/tex] is initially defined as:
[tex]\[
f(x) = 6x + 2
\][/tex]
We need to find [tex]\( f(x-3) \)[/tex]. This means wherever there is an [tex]\( x \)[/tex] in the function, we replace it with [tex]\( (x-3) \)[/tex].
2. Perform the substitution:
[tex]\[
f(x-3) = 6(x-3) + 2
\][/tex]
3. Distribute the 6:
Distribute the 6 inside the parentheses:
[tex]\[
f(x-3) = 6(x-3) + 2 = 6x - 18 + 2
\][/tex]
4. Combine like terms:
Combine the constants:
[tex]\[
f(x-3) = 6x - 18 + 2 = 6x - 16
\][/tex]
So, the final expression for [tex]\( f(x-3) \)[/tex] is:
[tex]\[
f(x-3) = 6x - 16
\][/tex]
Among the given options, the correct one is:
[tex]\( \boxed{6x - 16} \)[/tex].
