Question

Consider the tables created using an initial investment of $1,000 and quarterly compounding of interest.

Table A represents the function that models the total amount of one investment, a(x), based on the annual interest rate, x, as a percent.

Table B represents the function that models the interest rate, r(d), as a percent, based on the total amount at the end of the investment, d.





Use the values in the table to verify the relationship between the functions representing the investments. Which conclusion can be made?

The functions are inverses because the domain of Table A is the same as the range of Table B.
The functions are inverses because the range of Table A is different from the domain of Table B.
The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (x, y) for the other function.
The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.

Answer 1

The correct choice is the first one.

Reason: a(x) = 1000(1 + x/400)^4 and r(d) = 400((d/1000)^{1/4} − 1). For every (x, a(x)) in Table A there is the pair (a(x), x) in Table B, and algebraically r(a(x)) = x and a(r(d)) = d, so the two functions are inverses. Hence the domain of Table A matches the range of Table B (and vice versa).