Preview Activity 2.6.1. The equation y =(x-32) relates a temperature given in x degrees Fahrenheit to the corresponding temperature y measured in degrees Celcius. a. Solve the equation y = (x-32) for x to write x (Fahrenheit temperature) in terms of y (Celcius temperature). b. Let C(x) = (x - 32) be the function that takes a Fahrenheit temperature as in- put and produces the Celcius temperature as output. In addition, let F(y) be the function that converts a temperature given in y degrees Celcius to the temperature F(y) measured in degrees Fahrenheit. Use your work in (a) to write a formula for F(y). 134 NO 2 c. Next consider the new function defined by p(x) = F(C(x)). Use the formulas for F and C to determine an expression for p(x) and simplify this expression as much as possible. What do you observe? d. Now, let r(y) = C(F(y)). Use the formulas for F and C to determine an expression for r(y) and simplify this expression as much as possible. What do you observe? # 7[ W S H X #2 # So, E D C $ 4 R F 24 V % 5 T G B Y H &7 N U * 00 J 8 26 Derivatives of Innerse Functions M 9 K O H J P "" ... 911 1 + 11 ait W S nd X x 2.6 Derivatives of Inverse Functions e. What is the value of C'(x)? of F'(y)? How do these values appear to be related? E D C 4 R F V % 5 T G 6 B Als Y H & 7 N U 8 M 1 -0 K O V H 1 A L -O command P V .. option ?