For the funcations f(x) =2x-6 and g(x) =5x+1 which composition produces the greatest output

C. f(g(x)) produces the greater output.  

Step-by-step explanation:

ƒ(x) = 2x - 6

g(x) = 5x + 1

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

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

f(g(x)) - g(f(x)) = 10x - 4 - (10x -29) = 10x - 4 - 10x + 29 = 25

f(g(x)) is always 25 units greater than g(f(x)), no matter the value of x.

Thus f(g(x)) produces the greater output.