as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solve for "y".
[tex]\bf y = \cfrac{4}{x+7}\implies \stackrel{switcheroo}{\underline{x} = \cfrac{4}{\underline{y}+7}}\implies y+7=\cfrac{4}{x}\implies\qquad \stackrel{f^{-1}(x)}{y}=\cfrac{4}{x}-7[/tex]
