Then, determine whether $f$ and $g$ are inverses of each other.

Simplify. your answers as much as possible.

$($Assume that your expressions are defined for all $x$ in the domain of the composition You do not have to indicate the domain.$)$

$($a$)f(x)=-\frac{3}{x},x0$

$($b$)f(x)=x+2$

$g(x)=-\frac{3}{x},x0$

$g(x)=-x+2$

$f(g(x))=$

$f(g(x))=$

$g(f(x))=$

$g(f(x))=$

$f$ and $g$ are inverses of each other

$f$ and $g$ are inverses of each other

$f$ and $g$ are not inverses of each other

$f$ and $g$ are not inverses of each other