Results 1 to 3 of 3

Math Help - Range of a radical function

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    2

    Range of a radical function

    Hi everyone, I'm new here. I would appreciate it if someone can help me with this question. I need to find the range of the following function f(x) = (3x-2)^(1/2009). Thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Let g(x)=\sqrt[2009]{x}, \ h(x)=3x-2.

    Then f(x)=\sqrt[2009]{3x-2}=g(h(x)).

    g and h are continuous and strictly increasing, so f is continuous and strictly increasing.

    \lim_{x\to-\infty}f(x)=-\infty, \ \lim_{x\to\infty}f(x)=\infty.

    Then the range of f is \mathbb{R} (the set of real numbers).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    2
    Thank you so much, I was a bit confused with the graph of the function, it made it seem like the range was from -1 to 1, but it's just that the function is increasing very slowly. Thanks again!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A hard radical function
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 30th 2010, 07:52 PM
  2. The range of this function?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 17th 2010, 12:42 PM
  3. Radical function with no vertical asymptote
    Posted in the Algebra Forum
    Replies: 10
    Last Post: April 21st 2009, 06:04 PM
  4. Need the range of this function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 6th 2008, 06:40 PM
  5. Replies: 3
    Last Post: January 25th 2008, 02:57 PM

Search Tags


/mathhelpforum @mathhelpforum