Results 1 to 3 of 3
Like Tree2Thanks
  • 2 Post By skeeter

Thread: Proving that a function is odd

  1. #1
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    292
    Thanks
    2

    Question Proving that a function is odd

    Hey math forum folks,

    I know that f(x) = sinx is an odd function. With this knowledge, I therefore know that f(x) = sinx + x is also an odd function. However, I want to be able to prove that and I'm not sure how because I face the challenge with having to add sin pi/2 + pi/2 which I have no clue how.

    I attached an image to what I have done so far (I apologize for the messy appearance).

    I hope someone can help!

    - Olivia

    Proving that a function is odd-17349093_1341269359262488_100537034_o.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,155
    Thanks
    3672

    Re: Proving that a function is odd

    if $f(-x) = -f(x)$ the function is odd ...

    $f(x) = \sin{x} + x$

    $f(-x) = \sin(-x) + (-x) = -\sin{x} - x = -(\sin{x}+x) = -f(x)$

    note ...

    $\sin(-x) = \sin(0-x) = \sin(0)\cos(x) - \cos(0)\sin(x) = 0 \cdot \cos(x) - (1) \cdot \sin(x) = -\sin(x)$
    Last edited by skeeter; Mar 18th 2017 at 07:28 PM.
    Thanks from topsquark and Archie
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Feb 2014
    From
    United States
    Posts
    1,741
    Thanks
    808

    Re: Proving that a function is odd

    $k(x)\ is\ an\ odd\ function \iff k(x) = -\ k(-\ x).$ Definition.

    $k(x) = -\ k(-\ x) \iff -\ k(x) = k(-\ x).$ Simply multiply equation by - 1.

    $\therefore k(x)\ is\ an\ odd\ function \iff -\ k(x) = k(-\ x).$

    $Let\ f(x)\ and\ g(x)\ be\ odd\ functions\ and\ h(x) = f(x) + g(x).$

    $h(-\ x) = f(-\ x) + g(-\ x) = -\ f(x) - g(x) = -\ \{f(x) + g(x)\} = -\ h(x).$

    $\therefore h(x)\ is\ an\ odd\ function.$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving that a function is equal to a big O function
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Feb 7th 2017, 12:36 PM
  2. Help with proving a function is not onto.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Sep 4th 2013, 05:24 PM
  3. Proving a function is onto.
    Posted in the Discrete Math Forum
    Replies: 20
    Last Post: Oct 12th 2011, 11:11 AM
  4. Proving an onto function
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: May 1st 2011, 04:02 PM
  5. Proving a function is one-to-one/onto
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Oct 5th 2009, 05:20 PM

Search Tags


/mathhelpforum @mathhelpforum