math experts only
Please respond to both POST1: and POST2: in at least 200 words each.
Initial post that both POST1: and POST2: are responding to.
Consider the following two functions:
- F(m): The average temperature in Fahrenheit during month (m) of the year.
- C(f): The conversion formula to calculate the temperature in Celsius based on the temperature in Fahrenheit (f).
For this discussion, your task is as follows:
- Calculate (C ∘ F) for the month of your choice.
- Discuss the meaning of the function (C ∘ F)(m).
- How does the composition of functions in parts (a) and (b) compare to (F ∘ C)(m)? Are they the same?
The month I will use to calculate will be F(August)=84.
In this example we are using two known functions to produce desired outputs. These are functions because for every input there is only one output.
a) C(F)=5/9*(F-32)= C(84)=5/9*(84-32)= 28.89
b) (C ∘ F)(m) is used to describe the function that converts F(m) from a average temperature in Fahrenheit to an average temperature in Celsius. In the above example F(August)=84 so we can substitute the value of F to find an equivalent output in Celsius.
c) (F ∘C)(m) would be used to convert the Average temperature in Celsius to Average temperature in Fahrenheit. This conversion would need a known value of C(m). That value would be an input into the function F(C).
For this example, I chose to calculate by birth month of February averaging 43 degrees Fahrenheit. Using c(f) = 5/9 (f-32)
A) The temperature in Celsius is calculated as:
c(43) = 5/9 (43-32)
=6.1 degrees Celsius
B) The function (C ∘ F)(m) is to take the average temperature, in Fahrenheit, from the months in a year and convert this into Celsius.
C) (C ∘ F) (m) would be different from (F ∘ C) (m). While (C ∘ F) (m) gives the average temperature of a particular month in Celsius, (F ∘ C) (m) converts visa versa.
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