Question

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)

Answer 1

`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).