# Algebra Emergency!!

posted by Jane

Find the inverse of f(x)=2x+1/x-1 and please VERIFY(CHECK) Thanks so much

1. Damon

y = (2x+1) / (x-1) I assume you mean

x = (2y+1)/(y-1)
x y -x = 2 y + 1
2 y - xy = -(x+1)
(2-x)y = -(x+1)
y = (x+1)/(x-2)

2. Damon

Now try a check
say x = 3 (do not use x = 1, undefined)
then
y = 7/2

now see if that reverses
if x = 7/2
y = (7/2 +1)/ (7/2 -2)
= (9/2) / (3/2)
y = 3
sure enough

3. Steve

that's a great anecdote, but a true verification means that you have to show that

(2[(x+1)/(x-2)]+1)/([(x+1)/(x-2)]-1) = x

4. Jane

Thank you guys the help is great

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