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Suppose a function f : R ? R is continuous with f(0) = 1. Show that...

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Advance Math

Suppose a function f : R ? R is continuous with f(0) = 1. Showthat if there is a positive number x0 for whichf(x0) = 0, then there is a smallest positive number pfor which f(p) = 0. (Hint: Consider the set {x | x > 0, f(x) =0}.)

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