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 and , where represents the total amount of sales, which composition function represents his commission, or ? Use to verify the results.
  1. Find the composition function and interpret the results in the context of the problem.
  2. Evaluate the function found in the previous step using the test value .
  3. Find the composition function and interpret the results in the context of the problem.
  4. Evaluate the function found in the previous step using the test value .
  5. Based on these results, which composition function represents Paul’s commission, or ?