Question

If the mappings f and g are given by $f=\left\{\right(1,2),(3,5),(4,1\left)\right\}$ and $g=\left\{\right(2,3),(5,1),(1,3\left)\right\}$, write $fog$.

Answer 1

Given that, $f=\left\{\right(1,2),(3,5),(4,1\left)\right\}$
and $g=\left\{\right(2,3),(5,1),(1,3\left)\right\}$

Now, $fog\left(2\right)=f\left\{g\right(2\left)\right\}=f\left(3\right)=5fog\left(5\right)=f\left\{g\right(5\left)\right\}=f\left(1\right)=2fog\left(1\right)=f\left\{g\right(1\left)\right\}=f\left(3\right)=5fog=\left\{\right(2,5),(5,2),(1,5\left)\right\}$