as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}~~ = ~~5+2x\implies \stackrel{quick~switcheroo}{x~~ = ~~5+2y}\implies x-5=2y\implies \boxed{\cfrac{x-5}{2}~~ = ~~\stackrel{f^{-1}(x)}{y}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(x)}{y}~~ = ~~4-\sqrt{2x-3}\implies \stackrel{quick~switcheroo}{x~~ = ~~4-\sqrt{2y-3}}\implies x+\sqrt{2y-3}=4 \\\\\\ \sqrt{2y-3}=4-x\implies \stackrel{\textit{squaring both sides}}{2y-3=(4-x)^2} \\\\\\ 2y=(4-x)^2+3\implies \boxed{\stackrel{f^{-1}(x)}{y}~~ = ~~\cfrac{(4-x)^2 +3}{2}}[/tex]
