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Math Help - Given that f(x)+2f(8-x)=4 for all real x values find f(2).

  1. #1
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    Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    hi everybody,

    I've been looking at this problem for a while.

    Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    Maybe I am missing something obvious.

    Can anyone help?

    Thanks in advance.
    Last edited by Melody2; January 22nd 2014 at 02:28 AM.
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  2. #2
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    Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    Quote Originally Posted by Melody2 View Post
    hi everybody,

    I've been looking at this problem for a while.

    Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    Maybe I am missing something obvious.

    Can anyone help?

    Thanks in advance.
    f(2)+2 f(6)=4 \Rightarrow

    f(6)+2 f(2)=4 \Rightarrow

    3f(2)+3f(6)=8 \Rightarrow

    f(2)+f(6)=\frac{8}{3}

    from the first equation

    f(2)=4-2f(6)

    plugging in

    4-2f(6)+f(6)=\frac{8}{3} \Rightarrow

    4-f(6)=\frac{8}{3}  \Rightarrow

    f(6)=4-\frac{8}{3}=\frac{4}{3}

    f(2)=4-2\cdot\frac{4}{3}=\frac{4}{3}
    Thanks from Melody2
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    Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    Quote Originally Posted by romsek View Post
    f(2)+2 f(6)=4 \Rightarrow

    f(6)+2 f(2)=4 \Rightarrow

    3f(2)+3f(6)=8 \Rightarrow

    f(2)+f(6)=\frac{8}{3}
    I am sorry Romsek but this doesn't make any sense to me.

    f(2) + 2f(6) = 4 Good, that's given
    but
    the next 2 lines are a mystery to me.
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    Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    Quote Originally Posted by Melody2 View Post
    I am sorry Romsek but this doesn't make any sense to me.

    f(2) + 2f(6) = 4 Good, that's given
    but
    the next 2 lines are a mystery to me.
    the first line is your expression with x=2

    the second line is the same w/x=6

    the 3rd line is the sum of the 1st and 2nd lines

    the 4th line simple divides both sides by 3.
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    Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).



    Of course. Thanks Romsek. I really appreciate it.
    Last edited by Melody2; January 22nd 2014 at 10:48 PM.
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  6. #6
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    Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    clear?

    Ah, I shouldn't have had a \Rightarrow after the first line.

    The first doesn't imply the second line.

    Sorry.
    Thanks from Melody2
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  7. #7
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    Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

    All sorted. Thanks. The arrow did confuse me but also I didn't understand what w/x meant . I thought it was some kind of ratio. lol
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