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Let f(x) = (x + 2)/(x - 2).  Find the inverse of the function f(x).

 May 23, 2020
 #1
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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!

:)

 May 23, 2020
 #2
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PS. here's a good youtube video about finding inverses! https://youtu.be/2zeYEx4eTdc?t=505

 May 23, 2020

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