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?

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xero099 xero099 · Answer 1 · 2020-11-09T05:20:27+01:00

Answer:

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

Step-by-step explanation:

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

[tex]c(r) = c\,\circ\,h (r) = c(h(r))[/tex] (Eq. 1)

Where:

[tex]c[/tex] - Price, measured in US dollars.

[tex]h[/tex] - Packing time, measured in hours.

[tex]r[/tex] - Number of rooms, dimensionless.

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

[tex]c(r) = 40\cdot (4\cdot r)[/tex]

[tex]c(r) = 160\cdot r[/tex] (Eq. 2)

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