Question

Let $f:\{1,3,4\}\to \{1,2,5\}$ and $g:\{1,2,5\}\to \{1,3\}$
given by $f=\left\{\right(1,2),(3,5),(4,1\left)\right\}$ and $g=\left\{\right(1,3),(2,3),(5,1\left)\right\}$ write down $gof$

Answer 1

It is given that $f=\left\{\left(1,2\right),\left(3,5\right),\left(4,1\right)\right\}$ and $g=\left\{\left(1,3\right),\left(2,3\right),\left(5,1\right)\right\}$.

$gof\left(1\right)=g\left(f\left(1\right)\right)$

$=g\left(2\right)$

$=3$

$gof\left(3\right)=g\left(f\left(3\right)\right)$

$=g\left(5\right)$

$=1$

$gof\left(4\right)=g\left(f\left(4\right)\right)$

$=g\left(1\right)$

$=3$

Therefore,

$gof=\left\{\left(1,3\right),\left(3,1\right),\left(4,3\right)\right\}$