Results 1 to 2 of 2

Math Help - Inverse of a quadratic function

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Ghana
    Posts
    3

    Inverse of a quadratic function

    Hello everyone, I had to be stuck with a Maths teacher from hell...
    I was taught how to get the inverse of the following: 2x2 + 8x - 7 show at f-1(2)

    I understood the computations and interchanging and how it arrived at: 2y2 + 8y - 9 = 0

    However, my teacher used b2 - 4ac to arrive at 64 - 72 = -8, which is where my problem begins.

    I would like to know what testing for a perfect square has got to do with the inverse and how it proves it is or isn't an inverse.

    Also would like to know if it is bijective.

    I would be very greatful for explanations, my teacher doesn't explain anything and i think you guys are way better teachers.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,502
    Thanks
    765

    Re: Inverse of a quadratic function

    Quote Originally Posted by barbiedise View Post
    I was taught how to get the inverse of the following: 2x2 + 8x - 7 show at f-1(2)
    To talk about the inverse function, the original function f(x) = 2x2 + 8x - 7 must be injective. However, a quadratic polynomial considered as a function on all real numbers is not injective because a horizontal line can intersect the graph in two points. In particular, there are two values of x for which f(x) = 2.

    Quote Originally Posted by barbiedise View Post
    I understood the computations and interchanging and how it arrived at: 2y2 + 8y - 9 = 0

    However, my teacher used b2 - 4ac to arrive at 64 - 72 = -8, which is where my problem begins.
    The discriminant is 64 + 72.

    Quote Originally Posted by barbiedise View Post
    I would like to know what testing for a perfect square has got to do with the inverse and how it proves it is or isn't an inverse.
    This needs more context. Inverse of what and what is or is not an inverse? I am not sure what the connection is with testing for a perfect square. A question whether some n is a perfect square is a question about the existence of an integer (whose square is n), but the quadratic formula accepts and returns real numbers in general.

    Quote Originally Posted by barbiedise View Post
    Also would like to know if it is bijective.
    As a function from all reals to all reals, no quadratic polynomial is either injective (because the graph has two branches) or surjective (because the function has a minimum or a maximum).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inverse of 2 mod 108 and the quadratic equation
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: April 29th 2011, 11:49 PM
  2. Replies: 2
    Last Post: September 22nd 2009, 08:29 PM
  3. Inverse of Quadratic Function?
    Posted in the Algebra Forum
    Replies: 8
    Last Post: April 3rd 2009, 04:00 PM
  4. Domain and Range of the Inverse Quadratic Function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 29th 2009, 02:31 PM
  5. Replies: 2
    Last Post: March 30th 2008, 02:28 PM

Search Tags


/mathhelpforum @mathhelpforum