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Math Help - Another functional equation

  1. #1
    MHF Contributor alexmahone's Avatar
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    Another functional equation

    Let X be the set of all positive integers greater than or equal to 8 and let f: X \to X be a function such that f(x + y) = f(xy) for all x \ge 4, y \ge 4. If f(8) = 9, determine f(9).
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    Moo
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    Hello,
    Quote Originally Posted by alexmahone View Post
    Let X be the set of all positive integers greater than or equal to 8 and let f: X \to X be a function such that f(x + y) = f(xy) for all x \ge 4, y \ge 4. If f(8) = 9, determine f(9).
    f(9)=f(5+4)=f(20)=f(16+4)=f(64)

    f(8)=f(4+4)=f(16)=f(8+8)=f(64)

    Hence f(8)=f(9)
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