The formula f(x)= 9/5x + 32 is used to convert from x degrees Celcius to y degrees radian.?

Question

The formula g(x) = 5/9 (x - 32) is used to convert from x degrees Fahrenheit to y degrees Celsius. Can you explain how to show that f and g are inverse functions?

Answer 1

You need to show that f(g(x)) = g(f(x) = x

f(g(x)) = 9/5*[ 5/9 (x-32) ] +32 = x-32+32 = x

g(f(x)) = 5/9* [ (9/5x +32) - 32 = x+32-32 = x

So f(x) and g(x) are inverse functions.

Answer 2

"Degrees" in this case has nothing to do with angles or radians---it is temperature degrees we are talking about here.
The formula is to convert degrees C to degrees F.
Example 1
Convert 0° C to °F
f = (9/5) (0) + 32 = 32
ie 0° C = 32°F
Example 2
Convert 100°C to °F
f = (9/5)(100) + 32
f = 180 + 32
f = 212
ie 100°C = 212 °F