The Derivative of an Inverse Function
Remember… If a function f has an inverse function f -1, Then f (a) = b implies that f -1(b) = a.
Property of Inverse Functions:
The Derivative of f -1(x) = g(x): OR
Ex 1) Given that y = f(x) = x3 + 2x – 3 is a one-to–one function, and thus has an inverse, find (f -1)'(0).
Ex 2) Find , if: & .
Ex 3) Let g be the function which converts from Fahrenheit to Celsius. Then g (F) = C = (5/9) (F – 32) Find g -1:
Ex 4) Find , if: , , & .