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.