Results 1 to 5 of 5

Thread: Domain and polynomial degree

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

    Question Domain and polynomial degree

    Hi,

    I hope someone can help. So I have the following function h(x) = f(x)\cdot (1/f(x)).

    I'm trying to understand if the degree in the function changes why the domain would be different.

    For example, let's say that f(x) = (x^2)-25...the domain for h(x) would be all real numbers such that x doesn't equal 5 or -5.

    But what would the domain be if it was to the power of 3 instead of 2 (e.g. f(x) = (x^3)-25)? I would think that the domain would be all real numbers such that x doesn't not equal 5^(2/3), but I don't see this being represented as a hole when I use graphing technology - this makes me skeptical whether my thinking is right about this domain which has a power of 3.

    Please let me know.

    - Olivia
    Last edited by otownsend; Jun 26th 2017 at 01:03 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,967
    Thanks
    1140

    Re: Domain and polynomial degree

    Quote Originally Posted by otownsend View Post
    Hi,

    I hope someone can help. So I have the following function h(x) = f(x)\cdot (1/f(x)).

    I'm trying to understand if the degree in the function changes why the domain would be different.

    For example, let's say that f(x) = x^2-25...the domain for h(x) would be x x \neg 5 and x \neg -5.

    But what would the domain be if it was to the power of 3 instead of 2? I would think that the domain would be x \neg 5^(2/3), but I don't see this being represented as a hole when I use graphing technology - this makes me skeptical whether my thinking is right about this domain which has a power of 3.

    Please let me know.

    - Olivia
    You are correct. The denominator cannot be zero. So, you cannot have $x^3-25=0$ or $x^3=25$. That occurs at $x=\sqrt[3]{25} = 5^{2/3}$. So, the domain would be $x \neq 5^{2/3}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,967
    Thanks
    1140

    Re: Domain and polynomial degree

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    292
    Thanks
    2

    Re: Domain and polynomial degree

    Okay sounds good. It also said in my textbook that if 'f' is of an even degree, there may be no values excluded from the domain... is this true? And if so, what is an example of this?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Mar 2017
    From
    Toronto
    Posts
    292
    Thanks
    2

    Re: Domain and polynomial degree

    Never mind, I understand now what I was confused about. All good. Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 4th Degree Polynomial
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Apr 18th 2017, 10:11 AM
  2. Second Degree Polynomial
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 28th 2014, 12:01 PM
  3. Polynomial of Degree 2
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: Jan 19th 2011, 03:20 PM
  4. 7th degree polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jan 24th 2009, 08:05 AM
  5. Polynomial of fifth degree
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 13th 2006, 08:25 AM

Search Tags


/mathhelpforum @mathhelpforum