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Condition at Inverse function

Mathematica Asked on May 19, 2021

My goal is to get inverse of -Log[1 – x]. But the result shows conditional expression.
Could I know Why the condition -[Pi] <= Im[y] < [Pi] shows? There wass no assumption at variable y.

u[x_] := -Log[1 - x]

x /. Solve[y == u[x], x][[1]]

And the result showed,

ConditionalExpression[1 - E^-y, -[Pi] <= Im[y] < [Pi]]

One Answer

Here is one way ...

u[x_] := -Log[1 - x]

Assuming[{Element[x, Reals], Element[y, Reals]}, x /. Solve[y == u[x], x][[1]]]

yields

1 - E^-y

Correct answer by mjw on May 19, 2021

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