F(x) = 2x + 2 and g(x) = 7x + 1, which composition produces the greatest output

The correct answer would be g(x).

Notice that g(x) has a greater slope than f(x), which would make the line, if it were to be graphed, steeper, which means it increases at a faster rate.

To prove that g(x) has a greater output, you can plug in values into x to see which equation has the greater output.

Let's start with the number 1:
2(1)+2=4
7(1)+1=8

Then you can try other numbers such as 10 to see if this trend continues:
2(10)+2=22
7(10)+1=71

As you have seen, g(x) appears to have the greater output.

Hope this helps!