To find [tex]\( f(x+3) \)[/tex] given the function [tex]\( f(x) = 4x + 2 \)[/tex], follow these steps:
1. Start with the given function:
[tex]\[
f(x) = 4x + 2
\][/tex]
2. To find [tex]\( f(x+3) \)[/tex], we need to substitute [tex]\( x+3 \)[/tex] in place of [tex]\( x \)[/tex] in the original function:
[tex]\[
f(x+3) = 4(x+3) + 2
\][/tex]
3. Distribute the 4 through the parentheses:
[tex]\[
f(x+3) = 4 \cdot x + 4 \cdot 3 + 2
\][/tex]
4. Perform the multiplication inside the parentheses:
[tex]\[
f(x+3) = 4x + 12 + 2
\][/tex]
5. Combine the constant terms:
[tex]\[
f(x+3) = 4x + 14
\][/tex]
Therefore, the correct expression for [tex]\( f(x+3) \)[/tex] is [tex]\( 4x + 14 \)[/tex].
Among the given options, the correct answer is:
[tex]\[ f(x+3) = 4x + 14 \][/tex]
