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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of:
f%28x%29+=+%28x%2B2%29%2F%28x-2%29 First, substitute:f%28x%29+=+y
y+=+%28x%2B2%29%2F%28x-2%29 Now interchange the two variables, x and y.
x+=+%28y%2B2%29%2F%28y-2%29 Now solve this for y. Multiply both sides by (y-2).
x%28y-2%29+=+y%2B2 Expand the left side.
xy-2x+=+y%2B2 Add 2x to both sides.
xy+=+2x%2By%2B2 Now subtract y from both sides.
xy-y+=+2x%2B2 Factor the y on the left side.
y%28x-1%29+=+2x%2B2 finally, divide both sides by (x-1).
y+=+%282x%2B2%29%2F%28x-1%29 and now replace y withf%5E-1%28x%29 to get:
highlight%28f%5E-1%28x%29+=+%282x%2B2%29%2F%28x-1%29%29
Now if you want to prove the answer is correct, then you must show that:
f%28f%5E-1%28x%29%29+=+x
f%28f%5E-1%28x%29%29+=+f%28%282x%2B2%29%2F%28x-1%29%29
Simplify.
f%28f%5E-1%28x%29%29+=+%28%282x%2B2%29%2B2%28x-1%29%29%2F%28%282x%2B2%29-2%28x-1%29%29
Cancel the 2's and simplify.
f%28f%5E-1%28x%29%29+=+2x%2F2
f%28f%5E-1%28x%29%29+=+x OK!

Answer by ankor@dixie-net.com(22740) About Me  (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 = %28%28x%2B2%29%29%2F%28%28x-2%29%29
Swap x with y and solve for y:
x = %28%28y%2B2%29%29%2F%28%28y-2%29%29
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 = %28%282x%2B2%29%29%2F%28%28x-1%29%29
:
f%28x%5E-1%29 = %28%282x%2B2%29%29%2F%28%28x-1%29%29; is the inverse