# 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.

Month (m)
F(m)
Month (m)
F(m)
Month (m)
F(m)
January
42
May
72
September
73
February
43
June
83
October
63
March
52
July
84
November
55
April
63
August
84
December
44

C(f): The conversion formula to calculate the temperature in Celsius based on the temperature in Fahrenheit (f).

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?

POST1:
Hello Class,
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).
POST2:
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)
=5/9(11)
=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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