SOLUTION: F is a function from R to R. f(x)=x+1/x-1 then find the inverse function of f(x)

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Question 889576: F is a function from R to R. f(x)=x+1/x-1 then find the inverse function of f(x)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
ASSUMING you really mean %28x%2B1%29%2F%28x-1%29:
-
x=%28y%2B1%29%2F%28y-1%29
x%28y-1%29=y%2B1
xy-x=y%2B1
xy-x-y=1
xy-y-x=1
y%28x-1%29-x=1
y%28x-1%29=x%2B1
highlight%28y=%28x%2B1%29%2F%28x-1%29%29

Maybe a graph of each would help to be sure.

Original f(x)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B1%29%2F%28x-1%29%2Cx%29


The worked inverse - which as algebraic expression is the same - would not be different. Observe the symmetry around the line y=x shown in green.