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R be in the range of f, that is, there exists x… Show more

R be in the range of f, that is, there exists x… Show more Let f : [a, b] → R be a continuous function, and k ∈ R be in the range of f, that is, there exists x ∈ [a, b] so that f(x) = k. Show that the set E = f −1 ({k}) is closed (for every sequence (xn)n∈N of elements in E, if xn → x, then x ∈ E). • Show less


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