Question

If the mappings $f$ and g are given by
$f$ = {(1, 2), (3, 5), (4, 1)},
g = {(2, 3), (5, 1), (1, 3)},
then write down pairs in the mappings f o g and g o f.

Answer 1

$gof\left(x\right)=g\left(f\right(1\left)\right)=g\left(2\right)=3$

$\therefore$ (1, 3) $ϵ$ gof

$g\left(f\right(3\left)\right)=g\left(5\right)=1$

(3, 1) $ϵ$ gof

$g\left(f\right(4\left)\right)=g\left(1\right)=3$

$\therefore$ (4, 3) $ϵ$ gof

$gof=(1,3),(3,1),(4,3)$

$\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right)$

$f\left(g\right(2\left)\right)=f\left(3\right)=5$

$\therefore$ (2, 5) $ϵ$ fog

$f\left(g\right(5\left)\right)=f\left(1\right)=2$

$\therefore$ (5, 2) $ϵ$ fog

$f\left(g\right(1\left)\right)=f\left(3\right)=5$

$\therefore$ (1, 5) $ϵ$ fog

$fog=(2,5),(5,2),(1,5)$