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General Approach for Inverse Function

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Let $ f(x)$ a function and $ f^{-1}(x)$ the inverse function to be determined.


1.) The domain of $ f(x)$ is the range of $ f^{-1}(x)$: $ D_{f}=\operatorname{Range}(f^{-1})$

2.) The range of $ f(x)$ is the domain of $ f^{-1}(x)$: $ \operatorname{Range}{f}=D(f^{-1})$

3.) Write in the functional equation $ y$ instead of $ f(x)$.

4.) Solve this equation for $ x$.

5.) Exchange the variables, i.e. write $ y$ instead of $ x$ and vice versa.

6.) Substitute $ y$ by $ f^{-1}(x)$.

(Authors: Jahn/Knödler)
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  automatically generated 7/ 8/2004