ScalingFunctions not working properly for x-axis

Question

I am trying to make a chart where the x-axis has a log scale and the y-axis is in reverse order. I tried to use LogLinearPlot, and I tried to combine it with ScalingFunctions. My code was:

LogLinearPlot[1/x, {x, 1, 1000}, ScalingFunctions->"Reverse"]

But this failed. So I tried using Plot and ScalingFunctions:

Plot[1/x, {x, 1, 1000}, ScalingFunctions -> {"Log", "Reverse"}]

That gave me an error as well. I noticed that ScalingFunctions works just fine when applied to the y-axis, as in:

Plot[1/x, {x, 1, 1000}, ScalingFunctions -> "Log"]
Plot[1/x, {x, 1, 1000}, ScalingFunctions->"Reverse"]

However, when I apply ScalingFunctions to the x-axis, it will give an error; for example:

Plot[1/x, {x, 1, 1000}, ScalingFunctions -> {"Log", Identity}]

Can anyone tell me what to do to get a reversed y-axis and a logarithmic x-axis at the same time?

Answer 1

At least in v8, the following:

Reap@Plot[1/x, {x, 1, 1000}, ScalingFunctions -> (Sow@## &)]

reveals that the only argument passed to ScalingFunctions is the y coordinate. So, it wont scale the x axis.

But instead you may post-process the ticks generated by default:

k[f_] := Show[#, AbsoluteOptions[#, Ticks] /. {x_, x_, y__} :> {x, -x, y}] &@
                                                                LogLinearPlot[-f[x], {x, 1, 1000}]
f[x_] := 1/x;
k[f]