Results 1 to 3 of 3

Math Help - Finding the range, radical in the denominator

  1. #1
    Junior Member
    Joined
    Mar 2014
    From
    Canada
    Posts
    28

    Finding the range, radical in the denominator

    Hi,

    I am trying to find the range of

    f(x) = 1 / [sqrt(x+3)]

    I know that the function is undefined when x+3 =< 0 so the domain is all x>-3
    As the denominator must be positive, i know that f(x) > 0 and i believe that is the range.

    I am having trouble knowing how I should set this out on paper / what my working should look like.

    Any help would be appreciated, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,225
    Thanks
    851

    Re: Finding the range, radical in the denominator

    Quote Originally Posted by andy000 View Post
    Hi,

    I am trying to find the range of

    f(x) = 1 / [sqrt(x+3)]

    I know that the function is undefined when x+3 =< 0 so the domain is all x>-3
    As the denominator must be positive, i know that f(x) > 0 and i believe that is the range.
    At one end of it's domain $f(x) \to \infty$ as $x \to -3$ from above.

    At the other end of it's domain $f(x) \to 0$ as $x \to \infty$

    So the range of $f(x)$ is $(0,\infty)$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    615
    Thanks
    249

    Re: Finding the range, radical in the denominator

    Hi,
    As you know, the range of a function f with domain D is the set $\{f(x):x\in D\}$. So for $f(x)={1\over\sqrt{x+3}}$ with $D=(-3,\infty)$, you think the range is $(0,\infty)$.

    You already observed that for $x\in D$, $f(x)\in(0,\infty)$. You're halfway there. Let $b\in(0,\infty)\text{ or }b>0$. Then set $x=-3+{1\over b^2}\in D$. Then $f(x)={1\over\sqrt{3+-3+1/b^2}}=\sqrt{b^2}=b$ and so $b$ is in the range.

    How did I magically choose x? Why I solved the equation $f(x)=b$ for x. Note however, that solving this equation for x does not say b is in the range until I verify this as above.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 18th 2012, 07:35 PM
  2. Replies: 9
    Last Post: January 21st 2011, 04:40 PM
  3. Replies: 6
    Last Post: November 18th 2010, 05:38 PM
  4. Range of a radical function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 20th 2009, 06:09 AM
  5. Replies: 3
    Last Post: January 25th 2008, 02:57 PM

Search Tags


/mathhelpforum @mathhelpforum