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.