Results 1 to 5 of 5

Math Help - Odd / Even Functions

  1. #1
    Senior Member bugatti79's Avatar
    Joined
    Jul 2010
    Posts
    461

    Odd / Even Functions

    Folks,

    How does one show that f(x)sin(x) is an even function?

    I attempt it be replacing x by -x ie

    f(-x)sin(-x) but sin(-x) =-sin(x) therefore

    f(-x)(-sin(x))=-f(-x)sin(x)?????


    ----------------------------------------------------


    For the odd function g(x)cos(x) I calculate by replacing x by -x ie

    g(-x)cos(-x) but cos(-x) = cos (x) therefore

    g(-x)cos(x)=-g(x)cos(x) hence odd because g(-x)=-g(x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    May 2010
    Posts
    1,030
    Thanks
    28
    How does one show that f(x)sin(x) is an even function?
    you forgot to tell us whether or not f(x) is an even function. I assume it is odd:

    f(-x)sin(-x) =-1*f(x)*-1*sin(x) = f(x)sin(x)


    For the odd function g(x)cos(x) I calculate by replacing x by -x ie

    g(-x)cos(-x) but cos(-x) = cos (x) therefore

    g(-x)cos(x)=-g(x)cos(x) hence odd because g(-x)=-g(x)
    agree.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member bugatti79's Avatar
    Joined
    Jul 2010
    Posts
    461
    Quote Originally Posted by SpringFan25 View Post
    you forgot to tell us whether or not f(x) is an even function. I assume it is odd:

    f(-x)sin(-x) =-1*f(x)*-1*sin(x) = f(x)sin(x)



    agree.
    No f(x) is even...sorry for lack of clarity!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    May 2010
    Posts
    1,030
    Thanks
    28
    the product of an even function and an odd function is an odd function.

    f(-x)sin(-x) = f(x)*-1*sin(x) = -f(x)sin(x).


    so you wont be able to show the product is even.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by bugatti79 View Post
    No f(x) is even...sorry for lack of clarity!
    Then it is not true.
    \text{If }f(x)\text{ is even then }f(x)\sin(x)\text{ is odd.}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 15th 2010, 06:50 PM
  2. Replies: 3
    Last Post: February 23rd 2010, 05:54 PM
  3. Replies: 11
    Last Post: November 15th 2009, 12:22 PM
  4. Replies: 7
    Last Post: August 12th 2009, 05:41 PM
  5. Replies: 1
    Last Post: April 15th 2008, 10:00 AM

/mathhelpforum @mathhelpforum