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.