Results 1 to 3 of 3

Math Help - Inverse functions

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    10

    Inverse functions

    What is the least value of a such that the function;
    g: [a, ∞) -> R, g(t) = (3t) / (5+t^2) has an inverse function?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by Mercy99 View Post
    What is the least value of a such that the function;
    g: [a, ∞) -> R, g(t) = (3t) / (5+t^2) has an inverse function?
    You should know that for the function to have an inverse, the function should be bijective. In one of the previous posts, you have found the critical points. From that post you can know the region in which the function is increasing\decreasing. You will observe that in t \in (-\infty, -\sqrt{5}), the function is decreasing, when t \in (-\sqrt{5},\sqrt{5}),the function is increasing and finally when t \in (\sqrt{5},\infty), the function is decreasing.

    This clearly means that a horizontal line will cut the graph at most twice unless we restrict the domain to one of the three regions. Clearly a = \sqrt{5} satisfies the given constraint.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    286
    Hi!Mercy99
    To find the inverse of a function first you should check the interval where the function is bijective.for your question its bijective at
    1)[-5^1/2,5^1/2]
    2)(-inf,-5^1/2]union[5^1/2+inf)
    inf=infinity
    since for your question is [a,+inf] so by using 2) a must be equal to 5^1/2
    I am attacing a rough image.
    Hope this helps.
    Attached Thumbnails Attached Thumbnails Inverse functions-image000.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. inverse functions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 22nd 2009, 04:58 PM
  2. Replies: 2
    Last Post: October 19th 2009, 02:47 AM
  3. inverse one-one functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 12th 2009, 04:06 PM
  4. inverse functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 27th 2009, 07:54 AM
  5. Functions and Inverse
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 16th 2009, 01:16 AM

Search Tags


/mathhelpforum @mathhelpforum