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# If the mappings f and g are given by$f\;=\;\{(1,2),(3,5),(4,1)\} \;and\;g=\{(2,3),(5,1),(1,3)\},write\;f\;o\;g$

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• $fog(x)=f(g(x))$ for all
$Given f=\{(1,2),(3,5),(4,1)$

$g=\{(2,3)(5,1)(1,3)\}$

$fog(x)=f(g(x)) \qquad for\;x \in \{2,5,1\}$

$(fog)(2)=f(g(2))$

$=f(3)=5$

$(fog)(5)=f(g(5))$

$=f(1)$

$=2$

$(fog)(1)=f(g(1))$

$=f(3)$

$=5$

Solution: $fog=\{(2,5),(5,2),(1,5)\}$

edited Mar 25, 2013 by meena.p