Since we can have any letters/variables for our functions it is not important what a temperature conversion is but how do we solve a composition of functions, which can become complicated fast. In other words, how do we de-compose (break up) a function into a composition of other functions? How do we make things simpler in order to find a solution?

3. How does the composition of functions in parts 1 and 2 compare to (F ∘ C)(M)? Are they the same? or are they inverse?

a). Composition of Celsius and Fahrenheit (result in Celsius):

(C ᵒ F)(M) = (C ᵒ F)(63) = C(F(63)) = C(63) = 5/9(63-32) = 5/9×31 = 155/9

b). Composition of Fahrenheit and Celsius (result in Fahrenheit):

(F ᵒ C)(M) = (F ᵒ C)(63) = F(C(63)) = F(155/9) = 9/5C+32 = 9/5×155/9+32 = 31+32 = 63