Question

Below two situations are described in words. In each case, decide

whether the situation could be represented by a one-to-one function. If so, then write a
statement that best describes the inverse function. If not, explain why.
a) The function that pairs the number of days since your birth with your age in years..
b) The function that pairs the speed of your car in miles per hour with the speed in
kilometers per hour.

Answer 1

(a)

If by "age in years" you mean that you only consider whole years, then this is not a one-to-one function, because you will have the same output for 365 inputs:

• If you're 0 to 364 days old, your age in years is 0
• If you're 365 to 729 days old, your age in years is 1
• ....

So, you can see that it is not true that every different input yields a different output.

(b)

This is a one-to-one function: since one mile is 1.609 kilometers, you can convert miles per hour into kilometers per hour by multiplying by 1.609:

x mph = 1.609x km/h

The inverse function would be

x km/h = x/1.609 mph.