Let S = {1, 2, 3}. Determine whether the func | vedclass

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(B) function $f: S \rightarrow S$ is invertible if and only if it is a bijection (both one-one and onto). Given $f = \{(1, 1), (2, 2), (3, 3)\}$,we ob

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$f$ is invertible and $f^{-1} = \{(1, 1), (2, 2), (3, 3)\}$.

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(B) function $f: S \rightarrow S$ is invertible if and only if it is a bijection (both one-one and onto). Given $f = \{(1, 1), (2, 2), (3, 3)\}$,we observe that each element in the domain $S$ is mapped to a unique element in the codomain $S$,and every element in the codomain has a pre-image. Thus,$f$ is one-one and onto. Since $f$ is a bijection,it is invertible. The inverse function $f^{-1}$ is obtained by interchanging the elements of the ordered pairs $(x, y)$ to $(y, x)$. Therefore,$f^{-1} = \{(1, 1), (2, 2), (3, 3)\} = f$.

Let $S = \{1, 2, 3\}$. Determine whether the function $f: S \rightarrow S$ defined as below has an inverse. Find $f^{-1}$,if it exists: $f = \{(1, 1), (2, 2), (3, 3)\}$.

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