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Find a formula for the inverse of the function.

f(x) = (1 - sqrt(x)) / (1 + sqrt(x))

Added Mon, 08 Jun '15

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First, replace f(x) with y for comfort.

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

Now solve for x.

>> y + y*sqrt(x) = 1 - sqrt(x)

>> y*sqrt(x) + sqrt(x) = 1 - y

>> sqrt(x) * (1 + y) = 1 - y

>> sqrt(x) = (1 - y) / (1 + y)

>> x = ((1-y) / (1+y)) ^2

switch x with y and vice versa to keep with the standard if you like.

Added Mon, 08 Jun '15

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