Question: Let E R and f : R R be continuous. Show that f(E) f(E). Here f(E) := {f(x) : x E} and A is the

Let E R and f : R R be continuous. Show that f(E) f(E). Here f(E) := {f(x) : x E}

and A is the closure of A, that is, x A if and only if there exists a sequence {xn}nN such that

xn A and xn x as n .

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