[Gnuplot-info] set nonlinear explanation in manual

[Leoš P. <leo...@gm...>]

The manual says, page 152, nonlinear:
The hidden axis remains linear. Coordinates along the visible axis are mapped by applying g(x) to hidden axis coordinates. f(x) maps the visible axis coordinates back onto the hidden linear axis.

Example:

     set xrange [1:1000]
     set nonlinear x via log10(x) inverse 10**x

I believe it is incorrect, the mapping from the invisible (linear) axis to the visible axis is given by f(x) not g(x) and vice versa for the inverse as is also obvious from the example.
Can someone please confirm this or explain why the statement in the manual should be correct.
Thank you.