Paul works 40 hours a week at an electronics store. He receives a weekly salary of $220, plus a 3% commission on his sales of more than $5,000. Last week, Paul sold enough to earn his commission. Given the functions [math]f(x) = 0.03x[/math] and [math]g(x) = x – 5000[/math], where [math]x[/math] represents the total amount of sales, which composition function represents his commission, [math](f ∘ g)(x)[/math] or [math](g ∘ f)(x)[/math]? Use [math]x = 6000[/math] to verify the results.
[list=1] [*]Find the composition function [math](f ∘ g)(x)[/math] and interpret the results in the context of the problem. [*]Evaluate the function found in the previous step using the test value [math]x = 6000[/math]. [*]Find the composition function [math](g ∘ f)(x)[/math] and interpret the results in the context of the problem. [*]Evaluate the function found in the previous step using the test value [math]x = 6000[/math]. [*]Based on these results, which composition function represents Paul’s commission, [math](f ∘ g)(x)[/math] or [math](g ∘ f)(x)[/math]? [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math III[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.