SOLUTION: if (x)=x/x-1 what is f^-1(x)

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Question 764130: if (x)=x/x-1 what is f^-1(x)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Write the function the way you mean it: f%28x%29=x%2F%28x-1%29

For easier use of notation, call the inverse of f to be g.

f%28g%28x%29%29=x=g%28x%29%2F%28g%28x%29-1%29 and also g%28f%28x%29%29=g%28x%2F%28x-1%29%29=x
The f%28g%28x%29%29 composition will be easier to work with.

x=g%28x%29%2F%28g%28x%29-1%29
x%28g%28x%29-1%29=g%28x%29
x%2Ag%28x%29-x=g%28x%29
x%2Ag%28x%29-g%28x%29=x
%28x-1%29g%28x%29=x
highlight%28g%28x%29=x%2F%28x-1%29%29, the inverse of f(x).

This will help you understand the justification, if not trying a few values in the two functions:
graph%28300%2C300%2C-8%2C8%2C-8%2C8%2Cx%2F%28x-1%29%29