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Math Help - Fonction

  1. #1
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    Fonction

    Hello Guys

    I Need some Help in Fonctions
    The function f is set to R:
    F (x) = 3x 4x ^ 2 -1/2

    1. Calculate f (-1), f (-1/2), f (1 / 2) and f (1) { i did this)
    2. Proving that the equation f (x) = 0 admits three distinct solutions, ranging from
    -1 And 1

    3. Let x = cos (alfa)
    Express cos3 (alfa), according to cos (alfa)
    2. Determiner solutions of the equation f (x) = 0


    my second question for x between 0 and 2pie, solve cos(4x)=sin(2x) {edit : i solved this No need to solve it again lol

    and my last question :
    Prove that the equation sinx -1/2 = 0
    In admits } 0, 2 (pi) {a unique solution

    Thanks In Advance
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  2. #2
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    Quote Originally Posted by iceman1 View Post
    ...
    and my last question :
    Prove that the equation sinx -1/2 = 0
    In admits } 0, 2 (pi) {a unique solution
    Hello,

    if I understand your question right you are looking for the solutions of

    \sin(x) - \frac12 = 0~,\ x \in\ [0, 2\pi ]~\iff~\sin(x)=\frac12

    Then you get 2 (two) solutions: x = \frac16 \cdot \pi~\vee~x = \frac56 \cdot \pi (see attachment)
    Attached Thumbnails Attached Thumbnails Fonction-lsg_sin_glg.gif  
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  3. #3
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    Thanks Mate , any help with the First question?? i only solved the first part

    Thanks
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  4. #4
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    Quote Originally Posted by iceman1 View Post
    I Need some Help in Fonctions
    The function f is set to R:
    F (x) = 3x 4x ^ 2 -1/2

    1. Calculate f (-1), f (-1/2), f (1 / 2) and f (1) { i did this)
    2. Proving that the equation f (x) = 0 admits three distinct solutions, ranging from
    -1 And 1
    Probably the reason no one has helped you with it is because the form is strange.

    Is this
    F(x) = 12x^3 - 1/2
    or
    F(x) = 12x^2 - 1/2
    or something else?

    Edit: to have 3 roots it's likely a cubic, but I would like verification of the form first.

    -Dan
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  5. #5
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    Quote Originally Posted by iceman1 View Post
    Hello Guys

    I Need some Help in Fonctions
    The function f is set to R:
    F (x) = 3x 4x ^ 2 -1/2

    1. Calculate f (-1), f (-1/2), f (1 / 2) and f (1) { i did this)
    2. Proving that the equation f (x) = 0 admits three distinct solutions, ranging from
    -1 And 1
    ...
    Hello,

    you mentioned 3 (three) distinct solutions. So I assume that your function reads:

    f(x) = 3x\left(4x^2-\frac12\right)

    You have to solve the equation f(x) = 0:

    3x\left(4x^2-\frac12\right) = 0 . A product of two factors equals zero if one factor equals zero:

    3x\left(4x^2-\frac12\right) = 0~\iff~3x = 0~\vee~4x^2-\frac12 = 0 Solve the equations for x. I've got: x = 0 \vee x= -\frac14 \cdot \sqrt{2}~\vee~x= \frac14 \cdot \sqrt{2}

    These three solutions belong to [-1, 1]
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  6. #6
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    Ah ok Thanks Guys
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