Find the inverse of these functions f(x) = 5 + 2x f(x) = 4 - √(2x - 3) ​

Question

Find the inverse of these functions


`f(x) = 5 + 2x`

`f(x) = 4 - √(2x - 3)`
​

Answer 1

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.

`\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-√(2x-3)\implies \stackrel{quick~switcheroo}{x~~ = ~~4-√(2y-3)}\implies x+√(2y-3)=4 \\\\\\ √(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}}`