functional style - Transform a list of functions to a composition

How do I apply a list of functions in a nested way?

Example:

functionList = {f1,f2,f3}


RequiredCommand[functionList,Pi]

such that the required command returns

f3[f2[f1[Pi]]]

or f1[f2[f3[Pi]]] (reversing the order is easy)

I'm searching for an efficient way.

Answer

You'll want Composition[] or ComposeList[] for the purpose:

ComposeList[{f1, f2, f3}, x]
   {x, f1[x], f2[f1[x]], f3[f2[f1[x]]]}

Composition[f3, f2, f1][x]
   f3[f2[f1[x]]]

Since OP wants to be able to feed a list:

(Composition @@ {f3, f2, f1})[x]
   f3[f2[f1[x]]]

Comments

plotting - Plot 4D data with color as 4th dimension

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plotting - Filling between two spheres in SphericalPlot3D

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plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

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