Function with condition

I am starting my adventure with Mathematica. I would like to know if is there possibility to create function described by formula for example f(x):=1+2^n where 2^n < x. I have problem with this condition. I tried something like f[x_]:=(1+2^n) && (2^n< x) but probably it's wrong way. I'll be gratefull for any help

Edit:

Ok, let's take the function described by f(x)=1+2^n where n is solution of inequality 2^(-n) <= |x-1| < 2^(1-n) (n is integer) and we can define f(1)=1.

so for example f(3)=1+2^(-1) because n=-1 is solution of 2^(-n) <= |3-1| < 2^(1-n).

I'd like to create a plot of this or similar function. I tried something like: f[x_]:= 1 + 2^(n) /; n = Reduce[{2^(-n) <= Abs[ x - 1] < 2^(1 - n)}, k, Integers] but without success. I don't know how correctly put n value.

Comments

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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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