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Thread: Problem

  1. #1
    Member
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    Chennai
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    Problem

    Hi

    Define

    $\displaystyle \[ g(x) = \left\{
    \begin{array}{lll}
    x+2 & if & \ -3 \leq x \leq -1 \\
    -x & if & -1 < x \leq 1, \\
    x-2 & if & 1<x \leq 3.
    \end{array}
    \right.
    \] $


    Now let $\displaystyle f(x)=g(x-6n)+ 2n $ for $\displaystyle 6n-3 \leq x \leq 6n+3 , \ n \in \mathbb{Z}$.Prove that f takes each of it values three times
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Berkeley, California
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    Quote Originally Posted by Chandru1 View Post
    Hi

    Define

    $\displaystyle g(x) = \left\{
    \begin{array}{lll}
    x+2 & if & \ -3 \leq x \leq -1 \\
    -x & if & -1 < x \leq 1, \\
    x-2 & if & 1<x \leq 3.
    \end{array}
    \right.
    $


    Now let $\displaystyle f(x)=g(x-6n)+ 2n $ for $\displaystyle 6n-3 \leq x \leq 6n+3 , \ n \in \mathbb{Z}$.Prove that f takes each of it values three times
    I'm tired and going to bed, but I fixed your latex.
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