Question

Renee was asked to find the inverse of f(x)=2x-4 and graph both the function and it’s inverse. She found f^-1(x)=x+2/4 as the inverse and graphed the following:

Explain whether or not Renee is correct.

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}~~ = ~~2x-4\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y-4} \\\\\\ x+4=2y\implies \cfrac{x+4}{2}=y=f^(-1)(x)`

so we have to tell Renee to stop eating those mushrooms from the backyard.

Check the picture below.