Since 32°F=0°C and 212°F=100°C, the equation that converts the Celsius to the Fahrenheit is written as follows:
f(C)=(9/5)C+32 (°F), C: temperature in Celsius ··· Eq.1 Thus, the inverse of Eq.1 is the function that converts the Fahrenheit to the Celsius. Put "y" for "f(C)", and solve the equation for C:
y=(9/5)C+32 Subtract 32 from both sides:
y-32=(9/5)C Multiply both sides by 5/9:
(5/9)(y-32)=C Exchange sides:
C=(5/9)(y-32) Put "f¯¹(y) for "C", getting the inverse function of Eq.1:
f¯¹(y)=(5/9)(y-32) Put "F" for "y":
f¯¹(F)=(5/9)(F-32)
Therefore, the equation that converts the Fahrenheit to the Celsius is:
f¯¹(F)=(5/9)(F-32) (°C), F:temperature in Fahrenheit