Mathematics

Problem

A school maintenance team uses two successive procedures to evaluate classroom conditions. • Procedure

f

converts the room temperature from degrees Celsius

C

to degrees Fahrenheit using

F=1.8C+32

. • Procedure

g

assigns a comfort index to any temperature

T

(in Fahrenheit) by

g(T)=\dfrac{T-60}{2}

. a. (i) Write an expression for

(g\circ f)(C)

and explain, in words, what physical quantity it represents. b. (ii) Write an expression for

(f\circ g)(C)

and explain its physical meaning. c. (iii) Are

(g\circ f)

and

(f\circ g)

identical as functions? Support your answer with symbolic work and a brief verbal explanation.