Results 1 to 2 of 2

Math Help - Proving that a function is not a polynomial

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Canada
    Posts
    1

    Proving that a function is not a polynomial

    Question: Prove that the function f(x) = \frac{x}{x^2 + 1} is not a polynomial.

    My attempt (for which I got no marks as "it's not a proof") was to define a polynomial function as \frac{P(x)}{Q(x)} where Q(x) is always equal to 1, and since x^2 + 1 does not equal to 1 for any given value of x, then it's not a polynomial.

    So how does one approach the question? I was thinking of rewriting f(x) = \frac{x}{x^2 + 1} as f(x0) = \dfrac{1}{x + \frac{1}{x}} = (x + \frac{1}{x})^{-1} and then, since a polynomial function has a degree n \geq 0, and this function has a degree -1, it is by definition not a polynomial. But is that really a proof either? Not sure what to do.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: Proving that a function is not a polynomial

    I think I would try assuming f(x) = P(x), where P(x) is a polynomial, and see if I could deduce a contradiction.

    We would then have

    (x^2+1) P(x) = x

    Hmmm...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving the root of a cubic polynomial
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 28th 2011, 11:12 AM
  2. Replies: 3
    Last Post: September 14th 2010, 03:46 PM
  3. proving the function is even
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 17th 2010, 06:05 AM
  4. Proving the form of a polynomial?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 5th 2009, 09:18 AM
  5. [SOLVED] Proving that a polynomial is 0
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: March 22nd 2009, 05:25 AM

Search Tags


/mathhelpforum @mathhelpforum