Question

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

Answer 1

Let's see which composition you can obtain:

$f(g(x))=2(5x+1)-6=10x+2-6=10x-4 \\ g(f(x))=5(2x-6)+1=10x-30+1=10x-29$.

You can see that graph g(f(x)) lies under the graph of f(g(x)), then the composition f(g(x)) produces the greatest output.