How can you tell if this function if invertible? And if so, how would you find the inverse function?

The function F = g(C) = 32 + 9/5C converts a temperature in degrees Celsius to degrees Fahrenheit.
( a ) Explain how you can tell that this function is invertible.
( b ) If it invertible, find the inverse function C= g^(-1) (F)

1 Answer
Nov 17, 2017

C = g^(-1)(F) = 5/9(F-32)

Explanation:

Given:

F = 32+9/5 C

Subtract 32 from both sides to get:

F-32 = 9/5 C

Multiply both sides by 5/9 and transpose to get:

C = 5/9(F-32)

Note that both of these steps are reversible, so the equation we have arrived at is exactly equivalent to the original equation.

The derived equation uniquely determines C for any given value of F, so defines a function, which is the inverse function:

g^(-1)(F) = 5/9(F-32)

Since we have found an inverse function, we have completed b) and proved a).