Results 1 to 6 of 6

Math Help - Even and odd composite functions.

  1. #1
    Junior Member
    Joined
    Oct 2011
    Posts
    58

    Even and odd composite functions.

    Ok so
    if f is even and g is even then fog is?

    f(x) = f(-x)
    g(x) = g(-x)

    f(g(x)) = f(g(-x))
    f(-g(x)) = f(g(x))
    f(-g(x)) = f(-g(-x))

    so f(-g(x)) = f(g(x) fog is even???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: Even and odd composite functions.

    Quote Originally Posted by fabio010 View Post
    ok so
    if f is even and g is even then fog is?
    F(x) = f(-x) & g(x) = g(-x)
    f(g(x)) = f(g(-x))
    f(-g(x)) = f(g(x))
    f(-g(x)) = f(-g(-x))
    so f(-g(x)) = f(g(x) fog is even???
    correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,657
    Thanks
    598

    Re: Even and odd composite functions.

    Hello, Fabio010!

    This is simpler than you think . . .


    \text{If }f\text{ is even and }g\text{ is even, then }f\!\circ\!g\text{ is?}

    We know that: . \begin{Bmatrix}f(\text{-}x) &-& f(x) \\ g(\text{-}x) &=& g(x)\end{Bmatrix}

    The question is: . \begin{Bmatrix}\text{Is }f\!\circ\!g \text{ even?} \\ \text{Does }f(g(\text{-}x)) \text{  equal }f(g(x))\,? \end{Bmatrix}


    Since g(\text{-}x) = g(x), we have: . f(g(\text{-}x)) \:=\:f(g(x)) . . . . Yes!

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2011
    Posts
    58

    Re: Even and odd composite functions.

    So if f is odd and g is odd then:

    fog is odd because:

    f(g(x)) not equal f(-g(x))
    since g(-x) = -g(x)
    and -f(g(x)) = f(-g(x))

    right?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Even and odd composite functions.

    If f is odd then f(-x)=-f(x), if g is odd then g(-x)=-g(x).

    Show: f(g(-x))=-f(g(x))
    f(g(-x))=f(-g(x))=-f(g(x))

    Therefore f\circ g is odd.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Oct 2011
    Posts
    58

    Re: Even and odd composite functions.

    Ok thanks for the help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Composite Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 5th 2009, 02:19 PM
  2. composite functions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 15th 2009, 07:09 PM
  3. Composite functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 27th 2008, 06:46 PM
  4. composite functions :o
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 7th 2008, 06:25 PM
  5. Composite functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 25th 2007, 10:06 PM

/mathhelpforum @mathhelpforum