help

hi guest!

 \(f(x)=\frac{x+2}{x-2}\)

To find the inverse, you can first replace f(x) for y. \(y=\frac{x+2}{x-2}\)

1. we replace the x with y.  \(x=\frac{y+2}{y-2}\)

2. cross multiply:

 \(x(y-2)=y+2\)

\(xy-2x=y+2\)

\(xy-y=2x+2\)

\(y(x-1)=2x+2\)

3. divide both sides by x-1: \(y=\frac{2x+2}{x-1}\)

And that's the answer! \(\boxed{y=\frac{2x+2}{x-1}}\)

i hope this helped you!

:)

PS. here's a good youtube video about finding inverses! https://youtu.be/2zeYEx4eTdc?t=505