Find the inverse for each of the following functions.

$f (x) = 4 x + 9$
$f^{-1}( x ) =$

$g(x) = 3 x^3 -12$
$g^{-1}( x ) =$

$\displaystyle h(x) = \frac{4}{x + 12}$
$h^{-1}( x ) =$

$j(x) = \sqrt[3]{x + 3}$
$j^{-1}( x ) =$