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Math Help - Period

  1. #1
    Super Member dhiab's Avatar
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    Period

    function , is a real number .

    1 ) Find the period of this function
    2 ) Give the exempl for .
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Image does not show, happens with a lot of your posts mate!
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by dhiab View Post
    function , is a real number .

    1 ) Find the period of this function
    2 ) Give the exempl for .

    This doesn't make any sense.
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  4. #4
    Senior Member pankaj's Avatar
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    The correct question is as follows:
    If f(x+a)=\frac{1}{2}+\sqrt{f(x)-(f(x))^2}
    then prove that
    f(x+2a)=f(x)
    (Moscow Olympiad,1950)

    Solution:

    Replace x by x+a in the above expression

    f(x+a+a)=\frac{1}{2}+\sqrt{f(x+a)-(f(x+a))^2}

     <br />
f(x+2a)=\frac{1}{2}+\sqrt{\frac{1}{2}+\sqrt{f(x)-(f(x))^2}-\left(\frac{1}{2}+\sqrt{f(x)-(f(x))^2}\right)^2}<br />

     <br />
f(x+2a)=\frac{1}{2}+\sqrt{\frac{1}{4}-f(x)+(f(x))^2}=\frac{1}{2}+\sqrt{\left(f(x)-\frac{1}{2}\right)^2}<br />

     <br />
f(x+2a)=\frac{1}{2}+f(x)-\frac{1}{2}<br />

     <br />
f(x+2a)=f(x)<br />


    There are two more questions of this type:

    (i)If f(x-1)+f(x+1)=f(x) ,then find one of the periods of f(x).

    (ii)If f(x-1)+f(x+1)=\sqrt{3}f(x),then find one of the periods of f(x)
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  5. #5
    Super Member dhiab's Avatar
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    Quote Originally Posted by VonNemo19 View Post
    This doesn't make any sense.
    Hello : exo :
    (Moscow Olympiad,1950)
    watch follow the sulution ci over Thank you

    Quote Originally Posted by pankaj View Post
    The correct question is as follows:
    If f(x+a)=\frac{1}{2}+\sqrt{f(x)-(f(x))^2}
    then prove that
    f(x+2a)=f(x)
    (Moscow Olympiad,1950)

    Solution:

    Replace x by x+a in the above expression

    f(x+a+a)=\frac{1}{2}+\sqrt{f(x+a)-(f(x+a))^2}

     <br />
f(x+2a)=\frac{1}{2}+\sqrt{\frac{1}{2}+\sqrt{f(x)-(f(x))^2}-\left(\frac{1}{2}+\sqrt{f(x)-(f(x))^2}\right)^2}<br />

     <br />
f(x+2a)=\frac{1}{2}+\sqrt{\frac{1}{4}-f(x)+(f(x))^2}=\frac{1}{2}+\sqrt{\left(f(x)-\frac{1}{2}\right)^2}<br />

     <br />
f(x+2a)=\frac{1}{2}+f(x)-\frac{1}{2}<br />

     <br />
f(x+2a)=f(x)<br />


    There are two more questions of this type:

    (i)If f(x-1)+f(x+1)=f(x) ,then find one of the periods of f(x).

    (ii)If f(x-1)+f(x+1)=\sqrt{3}f(x),then find one of the periods of f(x)
    Hello : Thank you for correction
    Last edited by mr fantastic; June 19th 2009 at 04:33 AM. Reason: Merged posts
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