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E is not a function. It is a number. You want Exp. Not E. Or you want to write E^(x) instead of E[x]. Begin by fixing this. InverseFunction[Exp][x] Log[x] One of the first steps to debugging an issue like this is to ask: "Does this function I defined seem to work?". You can test the function for some simple inputs and see that it doesn't work: (* ...


inversePolyGamma[y_] := x /. FindRoot[y == PolyGamma[x], {x, 1}]; Show[ Plot[PolyGamma[x], {x, 0, 3}, PlotRange -> {{-3, 3}, {-3, 3}}], Plot[inversePolyGamma[y], {y, -3, 1}] ]

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