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Question

Let $$A=\left\{ a,b,c,d \right\} $$ and $$f:A\rightarrow A$$ be given by $$f=\left\{ \left( a,b \right) ,\left( b,d \right) ,\left( c,a \right) ,\left( d,c \right)  \right\} $$, write $${f}^{-1}$$


Solution

We have, $$A=\{a,b,c,d\}$$ and 
$$f:A\rightarrow A$$ be given by $$f=\{(a,b),(b,d),(c,a),(d,c)\}$$

We know that, when the elements of a function when interchanged gives function.
$$\Rightarrow$$  $$f^{-1}=\{(b,a),(d,b),(a,c),(c,d)\}$$

Mathematics

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