a) Let S ? R, assuming that f : S ? R is a continuous...
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a) Let S ? R, assuming that f : S ? R is a continuous function,if the image set {f(x); x ? S} is unbounded prove that S is unbounded.
b) Let f : [0, 100] ? R be a continuous function such that f(0) =f(2), f(98) = f(100) and the function g(x) := f(x+ 1)?f(x) is equal tozero in at most two points of the interval [0, 100].
Prove that (f(50) ? f(49))(f(25) ? f(24)) > 0.
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