SOLUTION: I need help with inverse problems. What is the inverse of the function f(x)=x+2/x-2?

Question 205007: I need help with inverse problems. What is the inverse of the function f(x)=x+2/x-2?
Found 2 solutions by Earlsdon, ankor@dixie-net.com:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Find the inverse of:
First, substitute:
Now interchange the two variables, x and y.
Now solve this for y. Multiply both sides by (y-2).
Expand the left side.
Add 2x to both sides.
Now subtract y from both sides.
Factor the y on the left side.
finally, divide both sides by (x-1).
and now replace y with to get:

Now if you want to prove the answer is correct, then you must show that:

Simplify.

Cancel the 2's and simplify.

OK!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
What is the inverse of the function f(x)=x+2/x-2?
:
Write it:
y =
Swap x with y and solve for y:
x =
Multiply both sides by (y-2)
x(y-2) = y + 2
:
xy - 2x = y + 2
:
xy - y = 2x + 2
Factor out y on the left:
y(x-1) = 2x + 2
Divide both sides by (x-1)
y =
:
= ; is the inverse

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