Question

For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output? A. Both compositions produce the same output B. Neither composition produces an output. C. f(g(x)) produces the greatest output. D. g(f(x)) produces the greatest output.

Answer 1

F(g(x)) = 2(5x+1)-6 = 10x+2-6 = 10x-4

g(f(x)) = 5(2x-6)+1 = 10x-30+1 = 10-29

10x-4>10-29 because from f(g(x)) you subtract less quantity. 
The answer to your question is C. I hope that this is the answer that you were looking for and it has helped you.