Finding the index number on a stretched cartesian grid

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jonasboy
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Imagine I have a set of discrete points equally spaced out and indexed from 1 to n (a 1D grid). On a cartesian grid if the spacing, dx, is constant the index can be obtained simply by:

i = floor(x/dx)

That was pretty simple, now if the cartesian grid is stretched (i.e. dx is not constant), it is not clear to me how to go about finding the index analytically. I am guessing that since we know the grid analytically we should be able to find the index analytically regardless if the grid is stretched or not. Any thoughts?

Thanks in advance.
 

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Not entirely certain of the question but...
Suppose the grid points are given by xi = f(i), some suitably nice function f. Wouldn't the grid point next below x be floor(f-1(x))?