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

Answer 1

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)

Answer 2

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

Answer 3

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

Answer 4

Thank you guys the help is great