a) Let S ⊂ R, assuming that f : S → R is a continuous function,...

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 to zero in at most
two points of the interval [0, 100].

Prove that (f(50) − f(49))(f(25) − f(24)) > 0.

Expert Solution

Colby Messinger answered 2 years ago

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