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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 fog.
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We have, $\mathrm{f}=\{(1,2),(3,5),(4,1)\}$
and $g=\{(2,3),(5,1),(1,3)\}$
Now, $\quad$ fog $(2)=\mathrm{f}\{\mathrm{g}(2)\}=\mathrm{f}(3)=5$
fog $(5)=f\{g(5)\}=f(1)=2$
fog $(1)=f\{g(1)\}=f(3)=5$
fog $=\{(2,5),(5,2),(1,5)\}$
and $g=\{(2,3),(5,1),(1,3)\}$
Now, $\quad$ fog $(2)=\mathrm{f}\{\mathrm{g}(2)\}=\mathrm{f}(3)=5$
fog $(5)=f\{g(5)\}=f(1)=2$
fog $(1)=f\{g(1)\}=f(3)=5$
fog $=\{(2,5),(5,2),(1,5)\}$
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