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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let \(f:\{1,3,4\} \to \{1,2,5\}and\;g:\{1,2,5\}\to\{1,3\}\) be given by \(f = \{(1, 2), (3, 5), (4, 1)\} \;and\; g = \{(1, 3), (2, 3), (5, 1)\}\). Write down \(gof\).

$\begin{array}{1 1} gof =\{(1,4),(3,1),(4,3)\} \\ gof =\{(1,4),(3,1),(4,3)\} \\ gof =\{(1,3),(3,1),(4,5)\} \\gof =\{(1,3),(3,2),(4,3)\} \end{array} $

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  • Given two functions $f:A \to B $ and $g:B \to C$, then composition of $f$ and $g$, $gof:A \to C$ by $ gof (x)=g(f(x))\;for\; all \;x \in A$
It is given that $ f: \{1,3,4\} \to \{1,2,3 \}$ and $ g: \{1,2,5\} \to \{1,3 \}$
$\Rightarrow$ The functions $f, g$ are defined by $ f= \{(1,2),(3,5),(4,1)\} $ and $ g=: \{(1,3),(2,3),(5,1)\} $
We know that given two functions $f:A \to B $ and $g:B \to C$, then composition of $f$ and $g$, $gof:A \to C$ by $ gof (x)=g(f(x))\;for\; all \;x \in A$
$\Rightarrow$ $ gof(1)=g(f(1))=g(2)=3$
$\Rightarrow$ $ gof(3)=g(f(3))=g(3)=1$
$\Rightarrow$ $ gof(4)=g(f(4))=g(1)=3$
From the above syeps we see that the composition of two functions gof is defined by $ gof =\{(1,3),(3,1),(4,3)\}$
answered Mar 19, 2013 by thagee.vedartham
edited Mar 19, 2013 by balaji.thirumalai
 

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