Question

The function ‘t’ which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = (9/5) C + 32. Find, 

(i) t(0) 

(ii) t(28) 

(iii) t(-10) 

(iv) the value of C when t(C) = 212 

(v) the temperature when the Celsius value is equal to the Fahrenheit value.

Answer 1

Given t(C) = 9C/5 + 32

(i) t(0) = 9(0)/5 + 32

= 32° F

(ii) t(28) = 9(28)/5 + 32

= 252/5 + 32

= 50.4 + 32 

= 82.4° F

(iii) t(-10) = 9(-10)/5 + 32

= -18 + 32 

= 14° F

(iv) t(C) = 212

9C/5 + 32 = 212

9C/5 = 212 - 32

= 180

9C = 180 x 5

C = (180 x 5)/9

= 100° C

(v) Consider the value of C be “x”

t(C) = 9C/5 + 32 

x = 9x/5 + 32 

5x = 9x + 160 

-160 = 9x – 5x 

-160 = 4x 

x = -160/4 = -40 

The temperature when the Celsius value is equal to the fahrenheit value is -40°