Question

Let $f:\{2,3,4,5\}\to \{3,4,5,9\}$ and $g:\{3,4,5,9\}\to \{7,11,15\}$ be functions defined as
$f\left(2\right)=3,f\left(3\right)=4$, $f\left(4\right)=f\left(5\right)=5$ and $g\left(3\right)=g\left(4\right)=7$ and $g\left(5\right)=g\left(9\right)=11$.
Find gof.

Answer 1

Given function:
$f:\{2,3,4,5\}\to \{3,4,5,9\}$ and $g:\{3,4,5,9\}\to \{7,11,15\}$
At $f\left(2\right)=3$ and $g\left(3\right)=7,gof\left(2\right)=g\left(f\right)2\left)\right)=g\left(3\right)=7$
At $f\left(3\right)=4$ and $g\left(4\right)=7,gof\left(3\right)=g\left(f\right)3\left)\right)=g\left(4\right)=7$
At $f\left(4\right)=5$ and $g\left(5\right)=11,gof\left(4\right)=g\left(f\right(4\left)\right)=g\left(5\right)=11$
At $f\left(5\right)=5$ and $g\left(5\right)=5,gof\left(5\right)=g\left(f\right(5\left)\right)=g\left(5\right)=11$
$\therefore gof=\left\{\right(2,7),(3,7),(4,11),(5,11\left)\right\}$