For each pair of functions $f$ and $g$ below, find $f(g(x))$ and $g(f(x)).$ 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 comp You do not have to indicate the domain.$)$

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

$($b$)f(x)=4x-7$

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

$g(x)=4x+7$

$f(g(x))=$

$f(g(x))=$

$g(f(x))=$

$g(f(x))=$

$f$ 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