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inverse_function [2013/06/25 15:45] nikolaj |
inverse_function [2013/06/25 15:46] nikolaj |
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| ==== Ramifications ==== | ==== Ramifications ==== | ||
| - | We have $\text{im}(f^{-1})=\text{dom}(f)=X$ as well as $\text{dom}(f^{-1})=\text{im}(f)$. | + | We have |
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| + | $\text{im}(f^{-1})=\text{dom}(f)=X,$ | ||
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| + | $\hspace{1cm} \text{dom}(f^{-1})=\text{im}(f).$ | ||
| Injectiveness of $f$ implies there is a left "left inverse" of the function: $f^{-1}\circ f=\text{id}$. | Injectiveness of $f$ implies there is a left "left inverse" of the function: $f^{-1}\circ f=\text{id}$. | ||
