If $f=\left\{\left(1,2\right),\left(2,3\right),\left(3,1\right)\right\}$ , then $fof$  is

$f\left[f\left(1\right)\right]=f\left(2\right)=3\Rightarrow \left(1,3\right)$

$f\left[f\left(2\right)\right]=f\left(3\right)=1\Rightarrow \left(2,1\right)$

$f\left[f\left(3\right)\right]=f\left(1\right)=2\Rightarrow \left(3,2\right)$

$\therefore$ $fof=\left\{\left(1,3\right),\left(2,1\right),\left(3,2\right)\right\}$