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The function may be extended to a function <math>[0,1] \to [-\infty,\infty]</math> with the value at 0 defined as <math>-\infty</math> and the value at 1 defined as <math>\infty</math>.

===Probabilistic interpretation~~=~~===

Given a probability <math>p</math> (strictly between 0 and 1) the inverse logistic function computes the logarithm of the corresponding odds. Explicitly, the odds corresponding to probability <math>p</math> are: