Results 1 to 7 of 7

Math Help - Domain of a expression involving a radical

  1. #1
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Domain of a expression involving a radical


    This is to confirm that my knowledge is correct on this point
    when the function has a radical like a sqrt and the interger is even (4) then the domain is equal to or greater then 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Domain of a expression involving a radical

    Yes, an even root must be a non-negative value to be real.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Domain of a expression involving a radical

    So in terms of this specific question the Domain would be (0,infinity) in interval notation
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Domain of a expression involving a radical

    No, you want to solve the inequality:

    x^2-5x\ge0

    You will find two intervals in the solution.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Domain of a expression involving a radical

    OK I get 0 and 5 as my two interval this means then my domain is all real number except 0 and 5 so in interval notation
    (-infinity,0) U (0,5) U (5, infinity)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Domain of a expression involving a radical

    You have found the correct critical numbers, but you need to test values within the sub-intervals (which are closed since we have a weak inequality):

    We have:

    x(x-5)\ge0

    a) (-\infty,0]

    We can pick any value in the interval not at the ends, let's pick x=-1. For this value, we look at the resulting signs of the two factors on the left of our inequality. This will give us two negative factors, meaning the expression is positive, so this interval is part of the solution.

    b) [0,5]

    Let's pick 1 as our test value. Now we have a positive factor and a negative factor, meaning the expression is negative, so this interval is not part of the solution.

    c) [5,\infty)

    Let's pick 6 as our test value. Now we have two positive factors, meaning the expression is positive, so this interval is part of the solution.

    Hence, the domain is:

    (-\infty,0]\,\cup\,[5,\infty)

    This is a general method, but in this case we could simply consider the graph of the parabolic radicand, and note that is is only negative on the open interval between its roots.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member M670's Avatar
    Joined
    Sep 2012
    From
    Montreal
    Posts
    142

    Re: Domain of a expression involving a radical

    Ohhh I see my mistake
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Radical Expression
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 9th 2011, 10:06 AM
  2. radical expression
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 10th 2010, 07:27 PM
  3. Radical Expression
    Posted in the Algebra Forum
    Replies: 6
    Last Post: April 29th 2010, 06:21 PM
  4. Help with radical expression!!!
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 10th 2008, 06:31 AM
  5. Divide radical expression
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 23rd 2008, 04:18 PM

Search Tags


/mathhelpforum @mathhelpforum