1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: The Inverse Function of f(x)=x^2+x

  1. Aug 21, 2011 #1
    I'm trying to work out the method of getting the inverse function of

    [itex] f(x) = x^2 + x [/itex]

    I already know the inverse but I would like to know the method used to obtain it. So far I have:

    Made f(x) = y:
    [itex]y = x^2+2[/itex]

    And then made y = x and x = y:

    And then I did this but I'm not sure if it's correct:

    Apparently the solution is this
    [itex]x(y) = 1/2 (-1±sqrt(4 y+1))[/itex]

    But I need to know the steps to get that. Hope you can help. :)
  2. jcsd
  3. Aug 21, 2011 #2
    OK, let's leave from here. What you did afterwards is correct, but it won't help.
    You have


    this is a quadratic equation in y, so it can be solved with the quadratic formula. What does that give you?
  4. Aug 21, 2011 #3
    Oooh right so

    a = 1
    b = 1
    c = -x

    [itex]y=-1\pm \sqrt{(1+4x)}/2[/itex]

    I think

    Also sorry, I really fail with these itex tags.
    Last edited: Aug 21, 2011
  5. Aug 21, 2011 #4


    User Avatar
    Science Advisor

    By the way, since a real valued function of a real variable is "single valued", that does not have a true "inverse". What you are saying is that you can divide it into two functions, on either side of the vertex of the parabola, one having inverse function [itex]f^{-1}(x)= (1/2)(-1+ \sqrt{4x+ 1})[/itex] and the other having inverse [itex]g^{-1}(x)= (1/2)(-1- \sqrt{4x+ 1})[/itex]
  6. Nov 29, 2011 #5
    try this:


    y(x) = a(x^2)+bx+c

    0 = a(x^2)+bx+(c-y)


    x(y) = (1/2a)(-b+(b^2 - 4a(c-y))^.5)

    which is just the general quadratic with c replaced by (c-Y) so that x becomes a function of y. Abel showed this can't be done in general for polynomials with a finite number of arithmatic operations.

    I would like to know how to the math symbols in something other than text. Is that what badballer was refering to in "itex tags"?
  7. Feb 7, 2013 #6
    I do not know the formula, but know the answer. Your function x^2+x looks like not-complete standart quadratic equation
    (where a^2=x^2, 2ab=x, but missing b^2),
    if it would be complete we could write it as
    To make it complete we add missing b^2,
    if our a=x and 2ab=x, then our b is 1/2.
    Our b^2 is 1/4, so we add it on both sides:
    Square root both sides:
    move 1/2 from left side to right
    Now you can transform right side of your equation to what you have
    Put 2 under square root:
    Then just do simple math
  8. Feb 7, 2013 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You have just answered a thread that is more than 1 year old.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook