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let F : R to R be a continuous function a) prove that the set {x...

let F : R to R be a continuous function

a) prove that the set {x in R:, f(x)>4} is open

b) prove the set {f(x), 1<x<=5} is connected

c) give an example of a function F that {x in r, f(x)>4} is disconnected

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