Example 6 - Prove that the identity function on real numbers f(x) = x
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SOLVED:(a) Prove that there does not exist a continuous function f defined on 𝐑 which takes on every value exactly twice. Hint: II f(a)=f(b) for af(a) for all x in (a, b) or f(x)b (b) Refine part (a) by proving that there is no continuous function f which takes on each value either 0 times or 2 times, i.e., which takes on exactly twice each value that it does tiake on. Hint: The previous lint implies that f las cither a natxinum or a niminum value (which must be taken on twice). What can be sai
SOLVED:(a) Prove that there does not exist a continuous function f d…
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