Question

A pharmaceutical salesperson makes $22,000 base salary a year plus 8% of the total dollars worth of products sold. Write a function S(x) that represents her yearly salary as a function of the total dollars x worth of products sold. Find S^(-1)(x). What does this inverse function tell you?

Answer 1

The function representing the yearly salary is S(x) = 22000 + 0.08x, and the inverse function S^{-1}(x) tells us the sales needed to achieve a particular salary.

Step-by-step explanation:

The function S(x) representing the yearly salary as a function of the total dollars worth of products sold by the pharmaceutical salesperson is S(x) = 22000 + 0.08x, where x is the total dollars worth of products sold, and 22000 is the base salary.

To find the inverse function, S^{-1}(x), we swap x and S(x) and solve for x. This gives us:

x = S^{-1}(x) = (x - 22000) / 0.08

The inverse function indicates how much in total dollar value of products needs to be sold to achieve a certain yearly salary x.

For instance, S^{-1}(30000) would give the total sales needed to earn a $30,000 salary.