Answer:
The expression that represents composition [tex](gof) (x)= 6x-3[/tex]
Step-by-step explanation:
Given functions:
[tex]f(x)=3x-2[/tex]
[tex]g(x)=1+2x[/tex]
To find [tex]g(f(x))\ or\ (gof)(x)[/tex]
Plugging in [tex]f(x)[/tex] in [tex]g(x)[/tex]
[tex]g(f(x))=1+2f(x)[/tex]
Substituting function [tex]f(x)=3x-2[/tex]
[tex]g(f(x))=1+2(3x-2)[/tex]
Using distribution.
[tex]g(f(x))=1+2(3x)-2(2)[/tex]
[tex]g(f(x))=1+6x-4[/tex]
[tex]g(f(x))=6x-3[/tex]
Thus the expression that represents composition [tex](gof) (x)= 6x-3[/tex]
