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I've got an interpolating function which has been generated from using NDSolve and I'm trying to find all the values of x for which the y value is equal to 2.

I've constructed a (much) easier example to show what I mean.

Suppose I have a set of points which I have generated an interpolating function from:

points = {{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}};

ifun = Interpolation[points]

which gives me:

InterpolatingFunction[{{0, 5}}, "<>"]

How would I then go about finding the x values in this function for which y is equal to 2?

The code I have tried is as follows:

Table[x /. FindRoot[ifun[x] == 2, {x, xInit}], {xInit, 0, 10, 1}]

but this produces a lot of errors and extrapolates beyond the limits of my interpolating function. Also, while this finds all the values in this particular example, once the interpolation function gets more complicated it's skipping roots and extrapolating far beyond my limits. Does anyone have any ideas? Thanks in advance

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# Find all roots of an interpolating function in Mathematica

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