For the functions f(x) = 2x + 2 and g(x) = 7x + 1, which composition produces the greatest output?

both compositions produce the same output.
neither composition produces an output.
f(g(x)) produces the greatest output.
g(f(x)) produces the greatest output.

First we have to find (f o g)(x):
(f o g)(x) = [2(7x + 1) + 2] = (14x + 2 + 2) = 14x + 4 
Then we have to find (g o f)(x):
(g o f)(x) = [7(2x + 2) + 1] = (14x + 14 + 1) = 14x + 15 
Comparing both the results:

(g o f)(x) > (f o g)(x)
According to above explanation,
D.g(f(x)) produces the greatest output, is the correct answer.

Are you trying to figure out the volume?