# RegionPlot returning a number

Bug introduced in 10.0 and persisting through 11.3.0.0 or later

I had updated my mathematica to version 10 few days ago. And I had been shocked by the following fact:

s = FunctionInterpolation[Sin[x], {x, 0, 1}];
RegionPlot[InverseFunction[s][x] <= y, {x, -1, 1}, {y, -1, 1}]
(* -1.13757 *)


Oh, my god! It is a number rather than a graph.

It seem like a bug about InverseFunction, FunctionInterpolation and RegionPlot because I then try another code:

s = FunctionInterpolation[Sin[x], {x, 0, 1}];
RegionPlot3D[InverseFunction[s][x] <= y z, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]


It certainly get the graph!

I later tried to use version 9 with the first code:

s = FunctionInterpolation[Sin[x], {x, 0, 1}];
RegionPlot[InverseFunction[s][x] <= y, {x, -1, 1}, {y, -1, 1}]


a graph got as well.

• Normally, bugs is reserved for when the community believes something is a bug, and should not be applied without that input. However, I'll confirm it, and it's certainly odd. Apr 11 '15 at 12:19
• I've reported it. Apr 11 '15 at 12:31
• I do not know if it was urgent but in waiting for a solution is this usefull ? Plot[{InverseFunction[s][x], x}, {x, -1, 1}, Filling -> {1 -> {{2}, {Red, None}}}] May 25 '16 at 3:47
• Still a problem under V11.0.0, though it now returns Show[-1.13757, DisplayFunction -> Identity] Aug 22 '16 at 18:41
• However, this works RegionPlot[InverseFunction[Sin][x] <= y, {x, -1, 1}, {y, -1, 1}]... Nov 11 '17 at 20:08

It is a bug (I tested on V11.1) and can be worked around by using Plot instead. For completeness I also demonstrate, how to get the edge back:
s = FunctionInterpolation[Sin[x], {x, 0, 1}]; 