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inverse_function [2013/06/25 15:44] nikolaj |
inverse_function [2013/06/25 15:46] nikolaj |
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We have | We have | ||
- | $\text{im}(f^{-1})=\text{dom}(f)=X$, | + | $\text{im}(f^{-1})=\text{dom}(f)=X,$ |
- | $\text{dom}(f^{-1})=\text{im}(f)$. | + | $\hspace{1cm} \text{dom}(f^{-1})=\text{im}(f).$ |
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: $f^{-1}\circ f=\text{id}$. |