The temperature F (in degrees Fahrenheit) corresponding to a temperature C (in degrees Celsius) is given by a linear relation.
(a) Write the function F=F(C) that converts a Celsius temperature to Fahrenheit.
(b) Obtain the inverse function C=C(F) that converts a Fahrenheit temperature back to Celsius.
(c) Show, by computing both appropriate compositions, that the two conversion formulae found in parts (a) and (b) are indeed inverses of each other.