How do you find the inverse function of $f(x)=x/(x+1)$ ?

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Answer 1 · 2015-10-31T23:32:21

Let $y = f(x)$ and rearrange to find an expression for $x$ in terms of $y$ , hence:

$f^-1(y) = y/(1-y)$

Let $y = f(x) = x/(x+1) = (x+1-1)/(x+1) = 1-1/(x+1)$

Then:

$1-y = 1/(x+1)$

Hence:

$1/(1-y) = x+1$

Hence:

$x = 1/(1-y)-1 = (1-(1-y))/(1-y) = y/(1-y)$

So $f^-1(y) = y/(1-y)$

How do you find the inverse function of f(x)=x/(x+1)f(x)=x/(x+1)?