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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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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 $x \in \{a,b,c,d\}$

 

 

answered Mar 1, 2013 by meena.p
edited Mar 27, 2013 by thagee.vedartham
 

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