Question

Deirdre works for a moving company. Her job includes giving clients a price for their move. Deirdre has one function, h(r) = 4r, which gives the number of hours h to pack up a number of rooms r. She has a second function, c(h) = 40h, that gives the price c for the number of hours of packing h. What is the function that gives the price c for a number of rooms r?

Answer 1

The function that gives the price
`c` for a number of rooms
`r` is
`c(r) = 160\cdot r`.

Explanation:

This problem shows a case of composition between two function, which is defined as follows:

`c(r) = c\,\circ\,h (r) = c(h(r))` (Eq. 1)

Where:

`c` - Price, measured in US dollars.

`h` - Packing time, measured in hours.

`r` - Number of rooms, dimensionless.

If we know that
`c(h) = 40\cdot h` and
`h(r) = 4\cdot r`, then the composite function is:

`c(r) = 40\cdot (4\cdot r)`

`c(r) = 160\cdot r` (Eq. 2)

The function that gives the price
`c` for a number of rooms
`r` is
`c(r) = 160\cdot r`.