Question

Find the inverse equation f^-1(x) from the equation above

Answer 1

as you should already know, to get the inverse relation of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

`\stackrel{f(x)}{y}=2+√(x-1)~~\implies ~~\stackrel{\textit{quick switcheroo}}{x = 2+√(y-1)}\implies x-2=√(y-1) \\\\\\ \stackrel{\textit{squaring both sides}}{(x-2)^2=y-1}\implies (x-2)^2+1=y\implies (x-2)(x-2)+1=y \\\\\\ \stackrel{F~O~I~L}{(x^2-4x+4)}+1=y\implies x^2-4x+5=\stackrel{y~\hfill }{f^(-1)(x)}`