Add bar legend for a different function

Questions
1

Hello everyone,
Here, I want to add bar legend showing values of g[t]. Is there any way to do it? Thanks in advance.

Open in Wolfram Cloud ↗
2

I would do it with DensityPlot:

g[t_] := t^3 + 3*t + 12;
DensityPlot[g[Norm[{x, y}]],
 Element[{x, y}, Annulus[{0, 0}, {1, 2}]],
 PlotLegends -> Automatic]
3

Note, Here I have plotted f[t] and I need bar legend showing g[t]. That is the main issue here.

4

Try this:

g[t_] := t^3 + 3*t + 12;
DensityPlot[g[Norm[{x, y}] - 1],
 Element[{x, y}, Annulus[{0, 0}, {1, 2}]],
 PlotLegends -> Automatic,
 ColorFunction -> "SolarColors"]