please give a explation for each sub question $(20$ points$)$

Suppose $g$:$AB$ and $f$:$BC$ where $A-\{1,2,3,4\},B-\{a,b,c\},C-\{2,7,10\},$ and $f$ and $g$

are defined by $g=\{(1,b),(2,a),(3,a),(4,b)\}$ and $f=\{(a,10),(b,7),(c,2)\}.$

$($a$)$ Find $f$@$g.$

$($b$)$ Find $f^{-1}.$

Solution: