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Math Help - [SOLVED] help me plz

  1. #1
    7thPath
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    [SOLVED] help me plz

    let f be a function that satisfies the statement
    f(u+v)=f(u)+f(v)+1-cos(uv)

    find f(0)

    show work

    good luck and thanks i am helpless on this one
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by 7thPath View Post
    let f be a function that satisfies the statement
    f(u+v)=f(u)+f(v)+1-cos(uv)

    find f(0)

    show work

    good luck and thanks i am helpless on this one
    not exactly sure what you are after here. but we have f(0) when u + v = 0 => u = -v, so we could write,

    f(0) = f(-v) + f(v) + 1 - cos(-v^2)

    but that doesn't really get us anywhere, i think. so let's try something else. what if i solved for f(u) first, and then plug in u = 0?

    f(u) = f(u + v) - f(v) + cos(uv) - 1

    if u = 0, we get:

    f(0) = f(v) - f(v) + cos(0) - 1 = 0

    so f(0) = 0

    the same thing happens if we solve for f(v) and let v = 0

    so i suppose f(0) = 0 is actually the answer
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  3. #3
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    Here is another to look at it.
    f(u) = f(u + 0) = f(u) + f(0) + 1 - \cos (u \cdot 0)
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