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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]]
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    $\begingroup$ Since x or y can be a complex number. InverseFunction[u] $\endgroup$
    – cvgmt
    Mar 24 at 12:35
  • $\begingroup$ Thank you for reply. but I wonder How to remove the conditions(= Is there a way to assume x and y as Real at Mathmatica for this case?) $\endgroup$
    – Soon
    Mar 24 at 13:51
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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
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