Mathematics

Problem

A temperature conversion rule is given by the function

F:\mathbb R\to\mathbb R

defined by

F(C)=\frac{9}{5}C+32,

where

C

denotes temperature in degrees Celsius and

F(C)

denotes the corresponding temperature in degrees Fahrenheit. a. (i) Prove that

F

is bijective. b. (ii) Determine the inverse function

F^{-1}

and state its domain and codomain. c. (iii) Suppose the codomain is restricted to

[32,212]

(the Fahrenheit images of water’s freezing and boiling points). With this new codomain, decide whether

F

remains injective and/or surjective. Give reasons.