Let $S =\{1,2,3\} .$ Determine whether the functions $f: S \rightarrow S$ defined as below have inverses. Find $f^{-1}$, if it exists. $f=\{(1,1),\,(2,2),\,(3,3)\}$
Let $S =\{1,2,3\} .$ Determine whether the functions $f: S \rightarrow S$ defined as below have inverses. Find $f^{-1}$, if it exists. $f=\{(1,1),\,(2,2),\,(3,3)\}$
It is easy to see that $f$ is one-one and onto, so that $f$ is invertible with the inverse $f^{-1}$ of $f$ given by $f^{-1}=\{(1,1),(2,2),(3,3)\}=f$
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