Question

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

Answer 1

According to question, we have
$f\left(1\right)=2,f\left(3\right)=5,f\left(4\right)=1$
and
$g\left(1\right)=3,g\left(2\right)=3,g\left(5\right)=1$
Now, let $y=gof$
$y=g\left(f\right(x\left)\right)$
when $f\left(1\right)=2,y=g\left(f\right(1\left)\right)=g\left(2\right)=3$

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

when $f\left(4\right)=1,y=g\left(f\right(4\left)\right)=g\left(1\right)=3$
So the composition function or $gof$ wll be $\{1,3\},\{3,1\},\{4,3\}$