The Derivative of an Inverse Function

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Presentation transcript:

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: , , & .