Question

Let $f:1,3,4\to 1,2,5$ and $g:1,2,5\to 1,3$ be given by $f=(1,2),(3,5),(4,1)$ and $g=(1,3),(2,3),(5,1)$. Write down $gof$.

Answer 1

The function $f:1,3,5\to 1,2,5$ and $g:1,2,5\to 1,3$ are defined as

$f=(1,2),(3,5),(4,1)$ and $g=(1,3),(2,3),(5,1)$

$gof\left(1\right)=g\left(f\right(1\left)\right)=g\left(2\right)=3$ as $\left[f\right(1)=2$ and $g\left(2\right)=3]$

$gof\left(3\right)=g\left(f\right(3\left)\right)=g\left(5\right)=1$ as $\left[f\right(3)=5$ and $g\left(5\right)=1]$

$gof\left(4\right)=g\left(f\right(4\left)\right)=g\left(1\right)=3$ as $\left[f\right(4)=1$ and $g\left(1\right)=3]$

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