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!
:)