Results 1 to 3 of 3

Math Help - polynomial functions

  1. #1
    Member grgrsanjay's Avatar
    Joined
    May 2010
    From
    chennai,tamil nadu
    Posts
    143
    Thanks
    1

    polynomial functions

    the number of polynomial functions F of degree >=1 satisfy F(x^2 ) = [F(x)]^2 = F(F(x)) is
    (A) 0
    (B) 1
    (C) 2
    (D) infinetly many
    Last edited by grgrsanjay; August 29th 2010 at 03:50 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by grgrsanjay View Post
    the number of polynomial functions F of degree >=1 satisfy F(x^2 ) = [F(x)]^2 = F(F(x)) is
    (A) 0
    (B) 1
    (C) 2
    (D) infinetly many
    I get answer (B).

    f(x^2) = f(x)f(x) = f(f(x))

    Consider just the part

    f(x^2) = f(f(x))

    So try x^2 = f(x).

    Verify that this does not contradict the other equality given.

    Given the constraint on the degree we cannot choose f(x) = 0 or f(x) = 1.

    It also happens that 2 is the only nonzero real number satisfying n*n = n+n. (Look at the exponent to see why I say this.)
    Last edited by mr fantastic; August 29th 2010 at 05:04 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member grgrsanjay's Avatar
    Joined
    May 2010
    From
    chennai,tamil nadu
    Posts
    143
    Thanks
    1
    so if the degree of polynomial can me anything the f(x)=0 can also be an answer
     f(x) = x^2 satisfy all three parts

    this unfortunately appeared in my maths Olympiad conducted yesterday
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polynomial functions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 12th 2009, 06:57 AM
  2. Polynomial functions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 28th 2009, 12:46 PM
  3. polynomial functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 14th 2008, 04:38 PM
  4. Polynomial Functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 3rd 2008, 01:07 PM
  5. Polynomial Functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 19th 2008, 05:56 PM

Search Tags


/mathhelpforum @mathhelpforum