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Mathematik-Online problems:

Problem 109: Derivation of the Inverse Function

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Show that for each of the following functions $ f$ an inverse function $ f^{-1}$ for the interval $ I=(-1,1)$ exists, and calculate $ (f^{-1})'(f(0))$.

a) $ f(x)=x^3+x+1$ b) $ f(x)=x^3-3x+3$
c) $ f(x)=\ln\,(4+2x-x^2)$      d) $ {\displaystyle{f(x)=\frac{1-x}{1+x}}}$

(Authors: Apprich/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004