I use Mathematica 9 and am having trouble understanding 1-dimensional FindRoot, which ought to be using Brent's interval method. Problems arise when my real functions have involved Undefined as an auxiliary.

For example,

step[x_] := If[x < 1, -1, 1] + x/7;

stepa[x_] := If[NumberQ[If[x < 1, 0, Undefined]], -1, 1] + x/7;

stepb[x_] := If[NumberQ[If[x > 1, 0, Undefined]], 1, -1] + x/7;

all define the same real function and give the same Plots, but

{FindRoot[step, {x, 0, 2}],

FindRoot[stepa, {x, 0, 2}],

FindRoot[stepb, {x, 0, 2}]}

yields 3 different answers, the last two not being in the initial interval [0,2]:

{{x -> 1.}, {x -> -7.}, {x -> 7.}}

Can anyone help? Howand why does Mathematica use the innards of the function definitions?

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