Example 3

Paul works 40 hours a week at an electronics store. He receives a weekly salary of $500, plus a 5% commission on his sales of more than $2,000. Last week, Paul sold enough to earn his commission. Given the functions [math]f(x) = 0.05x[/math] and [math]g(x) = x – 2000[/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 = 3000[/math] to verify the results.
[list=1][br][*]Find the composition function [math](f ∘ g)(x)[/math] and interpret the results in the context of the problem.[br][*]Evaluate the function found in the previous step using the test value [math]x = 3000[/math].[br][*]Find the composition function [math](g ∘ f)(x)[/math] and interpret the results in the context of the problem.[br][*]Evaluate the function found in the previous step using the test value [math]x = 3000[/math].[br][*]Based on these results, which composition function represents Paul’s commission, [math](f ∘ g)(x)[/math] or [math](g ∘ f)(x)[/math]?[br][/list]

Information: Example 3