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Thread: Another functional equation

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

    Let $\displaystyle X$ be the set of all positive integers greater than or equal to $\displaystyle 8$ and let $\displaystyle f: X \to X$ be a function such that $\displaystyle f(x + y) = f(xy)$ for all $\displaystyle x \ge 4, y \ge 4$. If $\displaystyle f(8) = 9$, determine $\displaystyle f(9)$.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by alexmahone View Post
    Let $\displaystyle X$ be the set of all positive integers greater than or equal to $\displaystyle 8$ and let $\displaystyle f: X \to X$ be a function such that $\displaystyle f(x + y) = f(xy)$ for all $\displaystyle x \ge 4, y \ge 4$. If $\displaystyle f(8) = 9$, determine $\displaystyle f(9)$.
    $\displaystyle f(9)=f(5+4)=f(20)=f(16+4)=f(64)$

    $\displaystyle f(8)=f(4+4)=f(16)=f(8+8)=f(64)$

    Hence $\displaystyle f(8)=f(9)$
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