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Let $f:A\rightarrow B\;and\;g:B\rightarrow C$ be the bijective functions.Then $(g\;o\;f)^{-1}$ is

\begin{array}{1 1}(A)\;f^{-1}\;o\;g^{-1} & (B)\;f\;o\;g\\(C)\;g^{-1}o\;f^{-1} & (D)\;g\;o\;f\end{array}

1 Answer

Toolbox:
  • A function h(x) is inverse of (gof) ie $h(x)=(gof)^{-1}$ if
  • $[(gof)oh](x)=x$
  • and $[ho(gof)](x)=x$
Let $h(x) be a mapping and assume h(x) is inverse of gof
 
we see that
 
$[(gof)oh](x)=gof(h(x))$
 
=x
 
$I_h$ h(x) is to be the inverse of gof then f[h(x)] must be $g^{-1}$
 
$gof(h(x))=x$ only if
 
$f(h(x)=g^{-1}$ and
 
=>$h(x)=f^{-1}(g^{-1})$
 
$=f^{-1}og^{-1}$
 
Hence 'A' option is correct

 

answered Mar 5, 2013 by meena.p
 

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