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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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