Manny is a plumber and charges $50 when he visits a client and $30 per hour for every hour he works. His bill can be expressed as a function of hours, x, with the function

f(x)= 50 +30x. Which statement explains the meaning of the inverse of the function?

A)Total bill as a function of the number of hours
B)Cost per hour as a function of the total bill
C)Number of hours as a function of the total bill
D)Total bill as a function of the cost per hour

The inverse function would be choice (C), since the two variables are total cost and number of hours.

E) None of the above!

The meaning of the inverse of the function is actually the opposite of all those options. It would be the function that gives you the number of hours worked based on the total bill. So the correct statement would be:

E) The inverse of the function gives the number of hours worked as a function of the total bill.

The inverse of a function is a new function that "reverses" the original function's operation. To find the inverse of a function, we usually swap the dependent and independent variables, and then solve for the new dependent variable.

In this case, the original function is f(x) = 50 + 30x. To find the inverse of f(x), we swap x and f(x) to get x = 50 + 30f^(-1)(x), where f^(-1)(x) represents the inverse function.

Now, let's analyze the options:

A) Total bill as a function of the number of hours: This is the original function, not the inverse.

B) Cost per hour as a function of the total bill: This is not the inverse either.

C) Number of hours as a function of the total bill: This represents the inverse function because it swaps the dependent variable (total bill) and the independent variable (number of hours). Thus, the answer is C) Number of hours as a function of the total bill.

D) Total bill as a function of the cost per hour: This is not the inverse function.

Therefore, C) Number of hours as a function of the total bill explains the meaning of the inverse of the function. It represents the number of hours worked based on the total bill charged by Manny.