To find [tex]\( f(x+3) \)[/tex] for the function [tex]\( f(x) = 6x + 2 \)[/tex]:
1. Start by substituting [tex]\( x+3 \)[/tex] into the function:
The function given is [tex]\( f(x) = 6x + 2 \)[/tex].
So, [tex]\( f(x+3) \)[/tex] means we need to replace every [tex]\( x \)[/tex] in [tex]\( f(x) \)[/tex] with [tex]\( (x+3) \)[/tex].
2. Substitute [tex]\( x+3 \)[/tex] into the function:
[tex]\[
f(x+3) = 6(x+3) + 2
\][/tex]
3. Distribute the 6 to both [tex]\( x \)[/tex] and 3:
[tex]\[
6(x+3) = 6x + 18
\][/tex]
4. Add 2 to the result:
[tex]\[
6x + 18 + 2 = 6x + 20
\][/tex]
So, the expression for [tex]\( f(x+3) \)[/tex] is:
[tex]\[
f(x+3) = 6x + 20
\][/tex]
Therefore, from the given options, the correct answer is:
[tex]\[
f(x+3) = 6x + 20
\][/tex]
