# Let A={a,b,c,d} and the function f={(a,b),(b,d),(c,a),(d,c)},Write $f^{-1}$.

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• $f^{-1}$ is the inverse function of $f:R \to R$ in set A. If $fof^{-1}(x)=x$ for all $x \in A$
If $A=\{a,b,c,d\}$

$f=\{(a,b),(b,d),(c,a),(d,c)\}$

we define $f^{-1}=\{(b,a),(d,b),(a,c),(c,d)\}$

$(fof^{-1})(a)=f(f^{-1}(a))$

$=f(c)$

=a

we see that

$(fof^{-1})(x)=x$ for all elements of $x \in \{a,b,c,d\}$

edited Mar 27, 2013