Question

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

Answer 1

Sorry for the wrong answer, this is the correct answer for it:

So, f(x)=2x-6 and g(x)=5x+1. First, I will do the f(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 of them have the same slope, but f(g(x)) have a greater y-intercept, which make it greater than g(f(x)). For instance, let x=1, so 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 help and fix my mistake.