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.