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Let g be continuous on an interval A and let F be the set of points where 9 fails to be one-to-one; that is,

Let g be continuous on an interval A and let F be the set of points where 9 fails to be one-to-one; that is, F = {x A: f(x) = f(y) for some y + x and y = A}. Show F is either empty or uncountable.

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