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    Question

    ┬аIf f(x) is continuous for all real values of

    x and f(x) takes on only rational values, then if f(1)=1, the value of f(0) is
    B 2 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D Cannot be determined Correct Answer Incorrect Answer
    E 3 Correct Answer Incorrect Answer

    Solution

    Property: - Let f:[0,1]тЖТ R be continuous such that f(x)тИИQ for any xтИИ[0,1] then f (x) is constant. Proof Suppose f isn't constant. Then for some a,bтИИ[0,1], f(a)тЙаf(b);┬а Without Loss of Generality, f(a)

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