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

For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output? both compositions produce the same result. no composition produces output. f(g(x)) produces the largest output. g(f(x)) produces the largest output.

g(f(x)) = 5(2x-6)+1 = 10x-30+1 = 10-29 10x-4>10-29 because from f(g(x)) you subtract less amount. The answer to your question is C. I hope this is the answer you were looking for and that it helped you.

. You can see that the graph of g(f(x)) is below the graph of f(g(x)), so the composite f(g(x)) produces the highest output.

f(g(x)) produces the largest output. g(f(x)) produces the largest output.

So f(x)=2x-6 and g(x)=5x+1. First I’m going to do of(g(x)), which is f(g(x))=2(5x+1)-6 => f(g(x))=10x+2-6 => f(g(x))=10x-4. And g(f(x))=5(2x-6)+1 => g(f(x))=10x-30+1 => g(f(x))=10x-29. Both have the same slope, but f(g(x)) has a larger intercept, making it greater than g(f(x)). For example, let x=1, then f(g(x))=10x-4 => f(g(x))=10(1)-4 => f(g(x))=10-4 = > f(g(x))=6, and g(f(x))=10x-29 => g(f(x))=10(1)-29 => g(f(x))=10 – 29 => g(f(x))=-19, and 6 is greater than -19, so f(g(x)) is greater than g(f(x)). Hope this helps and fixes my error.

What is the solution ?