For the functions f(x) = 2x − 6 and g(x) = 5x + 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.

What this is asking is which way of arranging these functions makes the biggest solution, or "output."

Remember that to solve something such as f(g(x)), we take the assigned value for x, solve g(x), and take the output for g(x) and plug it into f(x). 

By plugging the value of 1 into x, we can see that f(g(x)) will create the biggest output. As g(f(x)) will leave us with -19, whereas f(g(x)) will leave us with 6.